As was mentioned in Chapter 6, a couple is simply a pair of people who identify themselves in terms of belonging together, trusting one another, and having a unique relationship, separate from all others. A “We” is close to the same thing, yet it focuses on the relationship as an entity in itself. A “We” as shown in Figure \(\PageIndex{1}\) is a married couple but can also include cohabiters, or other intimate non-married couple arrangements. This is a relationship that is not intimately connected to any other relationships at the same profound level as they are connected to one another.
Here is a metaphor, a “We” is much like a vehicle (relationship) that two people purchased together. Both have to put in maintenance. Both have to care for it and treat it in such a way that it runs for a long time. Sometimes, spouses or partners attack the other in such a way that the other is harmed or damaged in their trust. A “We” is the social and emotional boundary a couple establishes when they decide to become a couple. This boundary includes only the husband and wife. It purposefully excludes the children, extended family, co-workers, and friends. Most couples who establish a strong marital bond have successfully distinguished themselves as a “We” and partially disengaged from the existing relationships of child, grandchild, best friends, etc.  You just have to establish a new exclusive intimacy that only includes you and your spouse (See Judith Wallerstein and Sandra Blakeslee (1995) The Good Marriage ISBN 0-446-67248-3; Warner Pub.) This also means making certain things into spouse-only issues which are the decisions, advice, and discussion that are held exclusively between partners and intentionally NOT between other family and friends. This might include types of birth control, how to run a budget, sexual techniques and practices, who might be at fault in an argument, etc. If a couple marries in their late 20's then they have a life-long history of intimate help-seeking and advice-giving relationships with others. These may continue as long as the help-seeking behavior doesn't violate the intimate agreements of confidentiality for each spouse or partner. I must emphasize how crucial it is to form the “We” so that married couples avoid the damaging intrusions of family and friends into their new marriage.
Marriage is a legal union between a man and a woman as recognized by most of the United States. Internationally and in certain US political regions, a man and another man or a woman and another woman can be legally recognized as a married couple. What are typical marriage structures? The US and world-wide culturally preferred marriage type today is monogamy. Monogamy is the marriage form permitting only one spouse at a time. Almost all in the US have married monogamously since the original colonies in the 1600s. Monogamy implies a 1:1 relationship and is typically desired both by married couples and by opposite and same-sex cohabiters.
Cohabitation is the heterosexual, bisexual, and homosexual moving in together of two partners without going through the formalities of legal marriage. Although similar in form and function, cohabitating couples live differently in many significant day-to-day aspects when compared to married couples. Also, many cohabiting couples eventually choose to marry, but their risk of divorce is higher than among couples that never cohabited. Cohabitation will be discussed more below, but it has been increasingly popular over the last 30 years.
Multiple spouses at the same time has been preferred in the past by Muslims, Africans, and Mormons (they ceased polygamy in 1890. Any current Mormons who try to marry polygamously are excommunicated) and Mormon-splinter groups (many are still polygamous today). Polygamy is a marriage form permitting more than one spouse at the same time. Polygyny is marriage form permitting more than one wife at the same time and is the most common form of polygamy in the world's history. Polygyny is still common and legal in many African, Middle-Eastern, Muslim, and Indian nations. It was a deep part of China's history and prior to World War II it was common for a Chinese man to have multiple wives and many children.
I have a former student who is 34 and was raised in a group that broke away from the Mormon congregation in the 1890's and formed its own polygamy-based religion. She came to guest lecture to my class and described her 45 siblings, 32 daughters and sons-in-law, 180 grandchildren, 32 great grandchildren, and typical meals at home of 40-53 family members per meal three times per day. Figure \(\PageIndex{2}\) shows her rough-sketched family genogram (she asked me to conceal identifiable aspects of her family so that they may be spared any ridiculing comments or embarrassment).
Her father biologically fathered about 46 children. He married his 16 year-old first wife in 1948 and had 16 children with her. Eleven years later he married his 21 year-old second wife and had 13 children with her. Eight years later he married an 18 year-old third wife and fathered 10 children with her. He then was asked to marry a 36 year-old divorcee who had 6 children from another marriage and they had one child together. He then married a 26 year-old and her 45 year-old sister who were widowed from the same husband. They together brought in 3 children from other marriages. He had 6 more children with his sixth wife. About 9 children are unrelated but consider him to be a fatherly figure. Interestingly, only 3 of all these children chose to marry polygamously.
When I asked my student why, she simply replied, “It's just too much work these days and it's not worth it to them.”
Polyandry
is a marriage form permitting more than one husband at the same time. This is historically and currently rare and if or when it was practiced, it often included the marriage of one wife to a set of brothers with all having sexual access to the wife.
Polyandry was found among some Pacific Island cultures and among the pre-Taliban Afghanis.
What if a person marries, divorces, marries, divorces, etc.? Serial Monogamy or Serial Polygamy is the process of establishing intimate marriage or cohabiting relationships that eventually dissolve and are followed by another intimate marriage or cohabiting relationship, that eventually dissolve, etc. in a series. So, polygamists have simultaneous multiple spouses while serial monogamists or serial polygamists have multiple spouses in a sequence of relationships. Millions of US adults will experience serial marriages and divorces. It often amazes me how much we love marriage in the United States. Many marry then divorce, yet still want to be married again. Many others who suffered through their parents' unhealthy marriages and divorces also want to marry, knowing firsthand how risky that might be.
Traditional roles of men and women influence how the power and marriage work out in society. Typically and throughout history families have been Patriarchal families where males have more power and authority than females and where rights and inheritances typically pass from fathers to sons. It should be mentioned that many family power structures still lean heavily toward male power.
Matriarchal families are where females have more power and authority than males and rights and inheritances pass from mothers to daughter and sons. In Matriarchal families, the mother is not only the social and emotional force of the family, but is also the economic force. More and more in the US families are leaning toward Egalitarian families which are families with power and authority more fairly distributed between husband and wife.
States have power when it comes to allowing marriage. The power held by states to legalize the economic, social, spiritual, emotional, or physical union or disunion of a man and a woman is not only traditional, but also enduring in US history. Centuries and millennia ago, fathers, clan or kinship leaders, religious leaders, and community members had the rights to marry which are now claimed by the state or nation. True, states don't get involved in the spiritual or physical union, they just license it or legalize it the same way they license drivers or certify the legal sale of property. Almost every year, there are about 2 legally sanctioned state marriages in the US for every 1 legally sanctioned state divorce decree.
In Figure \(\PageIndex{3}\) below you can see just how many legal marriages were granted per divorce for the years 1960-2005. These numbers are presented as a ratio (number of marriages/number of divorces per year). Between 1960 and 1970, there were almost 4 marriages per divorce, indicating nearly 4 marriages per 1 divorce nationwide (fewer divorces). As the rate of divorce increased in the 1970s-1980s we see that there were about 2 marriages per 1 divorce. Notice that since the late 1990s the ratio is increasing again because divorce continues to trickle downward.
For decades, newscasters and educators have warned that 1 in 2 marriages “end in divorce.” Sounds frightening, doesn't it? Is it true? Not really, since divorce never reached the actual 50 percent mark. Based on surveys of exactly how many people have ever been divorced in their lifetimes, most will tell you it is closer to 43 percent in the US's worst divorce rates ever (1980s). (see US Census for tables at www.census.gov/population/www...ed_tables.html).
The US Census Bureau conducts annual surveys of the US population and publishes them as the Current Population Surveys. Table \(\PageIndex{1}\) represents the US family Types as of October 1, 2008. You will notice that marrieds comprise the largest proportion of family types in 2008.  Next is divorced, widowed, then separated.
Table \(\PageIndex{1}\): US Family Types, 2008
Types
Numbers
Percentages
Married
123,671,000
52%
Widowed
14,314,000
6%
Divorced
23,346,000
10%
Separated
5,183,000
2%
Never Married - Single
71,479,000
30%
Total Families 15 and over
237,993,000
100%
Taken from the Internet on 30 March 2009 from Table A1. Marital Status of People 15 Years and Over, by Age, Sex, Personal Earnings, Race, and Hispanic Origin/1, 2008 www.census.gov/population/www...m/cps2008.html and see Table UC1. Opposite Sex Unmarried Couples by Labor Force Status of Both Partners: 2008 retrieved 30 March 2009 from www.census.gov/population/www/socdemo/hh-fam/cps2008.html
Look at Figure \(\PageIndex{4}\) below to see the US graphical trend of actual numbers in millions of family types. It shows that the single largest type of family in the US has always been marrieds then never marrieds. The divorced category overtook the widowed category in the 1970s and has been higher ever since. Why are the trends upward? Simple, these are numbers and not rates nor percentages. The population has grown and therefore the population size has been steadily increasing.
Robert and Jeanette Lauer are a husband-wife team who have not only studied the family but have written a college textbook called Marriage and Family: The Quest for Intimacy (2009, Cengage). They studied commitment and endurance of married couples. They identified 29 factors among couples who had been together for 15 years or more. They found that both husbands and wives reported as their number 1 and 2 factors that “My spouse is my best friend and I like my spouse as a person” (see 'Til Death Do Us Part: How Couples Stay Together 1986 by Robert Lauer and also Google Lauer and Lauer and Kerr various years). The Lauers also studied the levels of commitment couples had to their marriage. The couples reported that they were in fact committed to and supportive of not only their own marriage, but marriage as an institution.
Irreconcilable differences are common to marriage and the basic strategy to deal with them is to negotiate as much as is possible, accept the irresolvable differences, and finally live happily with them. Keeping a positive outlook on your marriage is essential. As was mentioned above, as long as a couple is married they are technically at risk of divorce.
 Would you still find them attractive today? Some who marry in their teens actually outgrow one another, including their loss of attraction that stems from their changed tastes. Couples who married as teenagers must unite as they take into account their ongoing maturation and change in tastes. When marital data is collected by the US Census Bureau, it often shows that those marrying in their teen years have the highest rates of having ever been divorced.
As is mentioned above, most unwed mothers end up marrying the biological father of their baby. These marriages often end in divorce more than marriages for non-pregnant newlyweds. The existence of children at the time of the wedding is often associated with higher divorce rates.
Family Scientists have borrowed from the physics literature a concept called entropy which is roughly defined as the principle that matter tends to decay and reduce, toward its simplest parts. For example, a new car if parked in a field and ignored, would eventually decay and rot. A planted garden, if left unmaintained, would be overrun with weeds, pests, and yield low if any crop.
Marital Entropy is the principle that if a marriage does not receive preventative maintenance and upgrades it will move towards decay and break down. Couples who take ownership of their marriage and who realize that marriage is not a state of constant bliss (nothing really is) and that it often requires much work, will experience more stability and strength when they nurture their marriage. They treat their marriage like a nice car and become committed to preventing breakdowns rather than waiting to repair them.
These couples read and study experts like Gottman, Cherlin, Popenoe, and others who have focused their research on how to care for the marriage, acknowledging the propensity relationships have to decay if unattended.
Many individuals struggle to completely surrender their single status. They mentally remain on the marriage market in case “someone better than their current spouse comes along.” Norval Glenn in 1991 argued that many individuals see marriage as a temporary state while they keep an eye open for someone better. “More honest vows would often be “as long as we both shall love” or “as long as no one better comes along (page 268).”
Glenn gets at the core of the cultural values associated with risks of divorcing. (See “The Recent Trend in Marital Success in the United States” by Norval D. Glenn Journal of Marriage and the Family, Vol. 53, No. 2 (May, 1991), pp. 261-270). In Figure 5 you can see the median duration of marriage for people 15 and older by sex and age. This data is exclusively for those who ended up divorcing. Even those who do divorce can expect a median (exact middle value in a list) of about 8 years for both men and women. The average couple could expect to stay married quite a long time.
A positive outlook for your marriage as a rewarding and enjoyable relationship is a realistic outlook. Some couples worry about being labeled naïve if they express the joys and rewards their marriage brings to their lives. Be hopeful and positive on the quality and duration of your marriage, because the odds are still in your favor. You've probably seen commercials where online matchmaking Websites strut their success in matching people to one another. There have been a few criticisms of online marital enhancement services, but millions have used them. Along, with DVD's, talk CDs, self-help books, and seminars there are many outlets for marital enhancement available to couples who seek them. Very few know that there is now a Website that offers support to marrieds who want to be proactive and preventative in their relationship marriage.eharmony.com/.
There also continues to be a trend of delaying first marriage until later in life. In 2005, the US median age at marriage was about 27 years for men (Washington DC was 29.9 factfinder.census.gov/servlet...ead_nbr=R1205& ds_name=ACS_2005_EST_G00_&-_lang=en&- redoLog=false&-mt_name=ACS_2005_EST_G00_R1204_US30&-format=US-30 ).
Marriage is very popular among US adults, in part because it does offer many rewards that unmarried people don't enjoy. A sociologist named Linda Waite co-wrote a book with Maggie Gallagher called The Case For Marriage: Why Married People Are Happier, Healthier, and Better Off Financially (2001, Doubleday). As its title implies, this book summarizes basic trends that have been found among married people for decades.
Marriage has become socially controversial in part because of the intense political efforts to legalize marriage for same-sex couples. Regardless of your moral position on the issue of same-sex marriage, you can see the political quest for it as an indicator of just how rewarding it is to be legally a “married couple.”
There are numerous studies and books on the benefits of marriage to married individuals. Table 2 lists 10 categories of these known benefits for you to consider.
Table \(\PageIndex{2}\): Ten Benefits of Being Married in Contrast to Being Single
Benefits of Being Married in Contrast to Being Single
1. Better physical and emotional health
2. More wealth and income
3. Positive social status
4.  Life-long continuity of intimate relationships
6. Safer circumstances for children
7. Longer life expectancy
8. Lower odds of being crime victims
9. Enhanced legal and insurance rights and benefits (tax, medical, and inheritance)
10. Higher self-reported happiness
Keep in mind as you think about this, that a toxic marriage has never been universally shown to be better than being unmarried or never married. It would be unwise to marry carelessly. It would also be unwise to think that once you marry you are at the end of your problems. A newlywed once told her mother that “now that I'm married, I'm at the end of all my problems.” Her mother wisely replied, “which end, Dear?” Marriage requires preventative, proactive, consistent, and timely maintenance to be rewarding and satisfying. The bottom line is that the burden of your marital quality falls to you and your spouse.
Cohabitation has been studied extensively for the last 3 decades, especially in contrast between cohabiting and married couples. Clear findings consistently show that cohabiting and marriage are two different creatures. Those who cohabit have less clarity on the intention and direction of the relationship than do marrieds. Also, people who cohabit then later marry are more likely to divorce than those who never cohabited. In 2010 the US Center for Disease Control reported that cohabitation is very common in our day:
www.cdc.gov/nchs/data/series/...3/sr23_028.pdf This report also stated that some of the cohabitation relationships dissolved while others transitioned to marriage. Less educated cohabiters cohabited longer while college-graduated cohabiters transitioned to marriage more.
There are a number of different ways of measuring cohabitation. The US Census Bureau reported about 6,209,000 US Unmarried-Partner households in 2007. Since a household in this case contains at least 2 persons we can derive 6,209,000 x 2= 12,418,000 unmarried adults sharing households. These data were extrapolated from the American Community Survey, and the types of Unmarried-Partner Households are identified in Figure \(\PageIndex{6}\) below.
Generally speaking cohabiting relationships are much more unstable than married ones (Popenoe (2009) and (Williams, K. et al 2008, For Better or For Worse? The Consequences of Marriage and Cohabitation for Single Mothers, Social Forces, Vol. 86, No 4, June page1481-1511). Popenoe (2009) is very clear about his argument that cohabiting is not as healthy in terms of the well-being of children as marriage has proven to be. He also identifies the trend of unmarried pregnancies that come with cohabitation trends.
Not all cohabitation experiences are the same. There are people who cohabit more than once.  These persons tend to be poorer and less educated in the US. When or if these persons ever marry, their divorce risks are over 2 times higher than those who never cohabited in a series (see Lichter, D.T. and Qian, Z. 2008, Nov. Vol 70 4, pages 861-878; J. of Marriage and Family).
This again confirms the belief among younger people in the US that cohabitation is normal or expected.
Figure \(\PageIndex{7}\). Percentage of Women 15-44 who were in a Union: Married or Cohabiting by Specific Age Categories.
Those cohabiters who get pregnant often have two choices. marry or break up. Breaking up is often more common than marrying (Lichter & Qian, 2008 page 863). Another recent study reported on lower commitment levels among cohabiting couples, and that the less religious were more likely to cohabit than marry (Stanley, S. M. et al, 2004 J. of Family Issues, Vol. 25, No. 4 496-519, “Maybe I Do Interpersonal Commitment and Premarital or Nonmarital Cohabitation”). Lichter and Qian (2008) reported that cohabiting couple's intention to marry plays into their relationship outcome. In other words, if they move in together thinking they will marry someday it may lead to a longer relationship as long as both have the same intention and neither changes their mind. Finally, there are known benefits to being married in a long-term relationship rather than being single, divorced, cohabiting, or other. Table \(\PageIndex{3}\) shows a quote taken from the cohabitation and marriage study referenced above called Marriage and Cohabitation in the United States: A Statistical Portrait Based on Cycle 6 (2002) of the National Survey of Family Growth.” Better mental and physical health with better medical insurance coverage proves to be a crucial quality of life factor for marrieds. As far as children are concerned, having better care and better adult outcomes among married people's children is also a crucial factor for parents and children.
Table \(\PageIndex{3}\): Health Benefits Known to be an Advantage Among Married Persons in the US
1. Generally better mental and physical health outcomes compared with unmarried persons (9)
2. Longer lives (10)
3. Higher rates of health insurance coverage (11)
4. Lower prevalence of cardiovascular disease (12) than unmarried persons
5. Better health and well-being of children
6. Children born to unmarried mothers are at greater risk for poverty, teen childbearing, poor school achievement, and marital disruption in adulthood than children born to married mothers (6,7,13-16)
There are also known financial benefits when comparing married to not-marrieds. More wealth accumulation, higher assets, and higher monthly income are consistent among marrieds. Figure \(\PageIndex{9}\) shows the 2007 annual earnings of marrieds compared to Single Men and Single Women income levels. The first thing you notice is that marrieds have consistently higher annual incomes. In 2007 specifically, marrieds had $28,231 more income than Single Men and $42,293 more than Single Women. The difference is even more pronounced if dual income married annual incomes are compared (e.g., in 2007 dual income couples had $86,435 which is $42,077 higher than Single Men and $56,139 more than Single Women).
b
Figure \(\PageIndex{9}\). Annual Income from 1990-2007 in 2007 Constant Dollars Comparing Marrieds to Single Men and Single Women
Table \(\PageIndex{4}\) summarizes the known benefits to marrieds over non-marrieds that have been established through numerous studies over the last 3 decades. Married people are safer and less prone to get into trouble than others. There is a buffering effect that accompanies having a life-long devoted spouse who helps deflect stress and hardships on a daily basis. Thus some of the health benefits of longer life, less suicide, more stable health coverage, and less illness and addiction. Also, marrieds have more social support, more continuity in long-term relationships, and especially more closeness for men in intimate family relationships. Husbands are less likely to abuse and be violent toward their wives than are boyfriends and partners. Married people have clear life-long goals and tend to buy homes, invest, and plan for retirement more than others. The government and military recognize spouses and reward them with tax breaks, benefits, and other sources of coverage and support more than others. In later life, many elderly report that their family relationships are very supportive and important to them. Studies show that the elderly enjoy their human investment in their children and grandchildren that yields emotional and social rewards throughout their golden years.
Table \(\PageIndex{4}\): Known Benefits Enjoyed by Married Couples in Comparison to Non-Married Persons
1. Less likely to become victims of crime
2. Less likely to commit crimes
3. Less addiction
4. Fewer accidents (especially among men)
5. Less suicide
6. Better stress management because spouse is a buffer to life's stresses
7. More social and emotional support (less loneliness)
8. More intimate connections to family members
9. Long-term continuity in family relationships of children, in-laws, grandchildren, etc.
10. Lower risk of domestic violence for women
11. Longer life expectancies
12.  More emotional and financial security (for both spouses)
14. Less uncertainty about direction of life and goals
15. More cost effective to live married versus single circumstances


39.1: Introduction to the Ears
By the end of this section, you should be able to:
- 39.1.1 Describe the structures and functions of the ears.
- 39.1.2 Identify common types of ear disorders.
Ear Structure and Function
The ear is connected to the central nervous system through inputs from the vestibulocochlear nerve —the eighth cranial nerve—which transmits sound from the inner ear to the auditory cortex in the temporal lobe of the brain. The vestibulocochlear nerve splits into the vestibular and cochlear nerves. The vestibular nerve controls motion and position; the cochlear nerve transmits signals from the cochlea to the temporal lobe in the brain so that sound can be heard. Sensorineural hearing loss (SNHL) is the most common type of hearing loss and accounts for the majority of all hearing loss. SNHL refers to any cause of hearing loss due to a pathology of the cochlea, auditory nerve, or central nervous system (Tanna et al., 2023).
The external ear, the middle ear, and the inner ear comprise the ear, as shown in Figure 39.2. The external ear—also called the outer ear, pinna, or auricle—structures include the ear lobe and cartilage. The external ear also consists of the external auditory canal , whose function is to transmit sound waves to the eardrum (also called the tympanic membrane). The external auditory canal gathers sound from outside the body and transmits it to the middle ear. This canal accumulates ear wax that typically self-cleans through daily chewing, grinding, and yawning motions (Sevy et al., 2023).
The tympanic membrane is the window from the outer ear into the middle ear. The middle ear consists of the tympanic membrane, tympanic cavity , and ossicles , which include three small bones: the malleus , incus , and stapes . The purpose of the middle ear is to transmit sound from the tympanic membrane to the inner ear. The tympanic cavity surrounds the three ossicles. The malleus, incus, and stapes transmit oscillatory vibrations from one small bone to another; the delicate stapes sends sound to the inner ear in a highly coordinated relay system. The tympanic membrane can rupture from infection, barotrauma, or the use of cotton swabs.
The Eustachian tube connects the middle ear to the back of the nose. It has three major functions:
- To protect the middle ear from infection
- To equalize air pressure on both sides of the eardrum for normal vibration
- To drain secretions from the middle ear
The inner ear is well protected within the temporal bone of the skull. The inner ear consists of the cochlea, the semicircular canals, and the vestibular and cochlear nerves. The cochlea translates sound waves into electrical impulses through mechanical stimulation of tiny hair cells that the brain can then interpret to recognize sounds. The semicircular canals sense head rotations to allow proprioception—the body’s ability to sense movement, action, and location—and balance. These canals contain fluid known as lymph and must be clear of debris such as small crystals called otoliths (Casale et al., 2023; Wang et al., 2020).
The inner ear is part of the central nervous system (CNS). Therefore, clients’ complaints about hearing can also be a sign of a more serious CNS disease process. The nurse should listen carefully to the client’s description of hearing issues and communicate concerns with the provider. Muffled hearing can represent a range of concerns from ear wax buildup to multiple sclerosis or neurosyphilis (Ramchandani et al., 2020). The nurse must also be aware of the ears’ structure and function, both within the parameters of normal function and when the client sustains a serious head injury or barotrauma.
Link to Learning
This 4-minute client education video describes the three parts of the ear: the external ear, the middle ear, and the inner ear.
Ear Disorders
This section describes common ear disorders for which pharmacological drops or solutions are prescribed. Selected common ear conditions for which systemic medications are prescribed will be reviewed as well.
Eustachian Tube Dysfunction and Post-Viral Syndrome
Barotrauma can result in a ruptured eardrum due to Eustachian tube dysfunction, which occurs when the air pressure in the middle ear does not equalize with ambient pressure. This can occur with sudden pressure changes, such as when flying or scuba diving. A ruptured eardrum can heal spontaneously or may require surgical intervention (Cleveland Clinic, 2022a). The Eustachian tube can become blocked during and after an upper respiratory infection as well. After an upper respiratory infection, the Eustachian tube may remain swollen, causing pain, muffled sound, or a feeling of fullness in the ear.
Tinnitus
Tinnitus is an ear disorder characterized by ringing or other annoying sounds in the ear. Tinnitus can be age-related, exacerbated by loud noises, or a result of circulation issues. Some medications can cause tinnitus, and hearing may not always fully return after stopping the medication. Medications associated with tinnitus include nonsteroidal anti-inflammatory drugs (NSAIDs), some antibiotics, anticancer medications, and antidepressants (Kim et al., 2021). The mechanism of these intrusive sounds is related to damaged hairs in the cochlea. Although there is no cure for tinnitus, there are treatments—including sound generators and stress management—that can help clients better cope with distracting sounds (Cleveland Clinic, 2022b; National Institute on Deafness and Other Communication Disorders, n.d.).
Ménière’s Disease
Ménière’s disease occurs when there is excess fluid in the inner ear. The cause is largely unknown. Ménière’s disease can have a hereditary component, or it can be triggered by viral or bacterial pathogens. This condition is characterized by hearing loss, vertigo, increased sweating, nausea, and vomiting. The nurse must implement fall precautions when caring for a client with Ménière’s disease because vertigo can predispose them to falls, including falls with injuries. There is no cure for Ménière’s disease, and though it does not affect life expectancy, it interferes with the client’s quality of life. Corticosteroids and antihistamines are offered as potential treatments and have varying effects (Webster et al., 2023).
Otitis Externa
Otitis externa (also known as swimmer’s ear) is an inflammation and/or infection of the external ear canal characterized by itchiness, pain, and a red ear canal. Otitis externa occurs in swimmers as well as older adults and those with poorly controlled diabetes. It can be exacerbated by using hearing aids, ear buds, and stethoscopes. The nurse should report client complaints of itchy, painful ear(s) to the provider because an untreated infection can spread to the bones and deep tissues of the ear canal and lead to skull osteomyelitis (Bruschini et al., 2019).
Otitis Media
Otitis media is an inflammation or infection of the middle ear. It typically occurs when the client has a cold, upper respiratory infection, or secondhand smoke exposure. Children are more likely to develop otitis media because of their horizontal Eustachian tube architecture, which increases the likelihood of fluid being trapped, causing an infection. Bottle feeding has been identified as a contributing factor to otitis media. Infants that breastfeed have fewer otitis media infections due to the oligosaccharides that are in breast milk, which function as prebiotics. These substances help infants develop their immune system to fight off infection.  Though the incidence of otitis media in adults is less, adults can also develop otitis media. Eustachian tube edema can narrow the diameter of the tube, allowing fluid to back up to the middle ear.
There are three major types of otitis media: acute otitis media, otitis media with effusion, and chronic otitis media with effusion (Johns Hopkins Medicine, n.d.). Acute otitis media is characterized by ear discomfort, in addition to systemic symptoms including fever and pain. Acute otitis media is frequently treated with systemic antibiotics, otic antibiotics, or a combination of both.
Otitis media with effusion occurs when some fluid remains after an infection has cleared and presents as fullness in the ear. Often decongestants or nasal steroids are prescribed to treat these symptoms. Antibiotics are not appropriate at this stage when no infection persists. The condition may become long-term and return although no infection is present.
Acute otitis media in adults can cause significant complications; therefore, adults are treated with antibiotic therapy (Limb et al., 2023). In general, antibiotic therapy is used more judiciously in children to avoid antibiotic resistance and side effects.
Benign Paroxysmal Positional Vertigo
Benign paroxysmal positional vertigo (BPPV) is a condition of the inner ear where otoliths—crystals of calcium carbonate—migrate into the inner ear fluid and cause a false sense of spinning. Otolith displacement occurs in older adults and those with a history of a blow to the head. BPPV is characterized by dizziness and a spinning sensation and may result in nausea and vomiting. Long after a head trauma, these symptoms can be triggered by a changing head position or keeping the head in one position for an extended period. Episodes can last for a few minutes and are disconcerting to the client, who is at risk of falling.
Special Considerations
Candida auris
Nurses must be aware of an emerging deadly fungal infection of the ear known as Candida auris . This fungal infection was first found in a Japanese person’s ear canal in 2009. Since then, there have been more than 3,000 systemic cases in the United States and more than 7,000 cases where the fungus has been found but has not yet caused infection (Centers for Disease Control and Prevention, 2023a, 2023b). C. auris must be reported to the Centers for Disease Control and Prevention (CDC) for tracking. Cases in the United States have occurred in health care settings largely among immunocompromised clients. Current treatment includes a drug class, echinocandins , that act on the Candida species. Echinocandins include anidulafungin ( Eraxis ), caspofungin ( Cancidas ), and micafungin ( Mycamine ).
(Source: Cândido et al., 2020)
Communicating with a Client with Hearing Impairment
There are different causes of hearing loss—including congenital hearing loss, aging, prolonged exposure to noise, and trauma—that are outside of the scope of this chapter. However, when treating clients with otic medications, the client’s hearing may be impaired by these medications or by the underlying ear condition the nurse is treating. The following guidelines can assist the nurse when working with these clients (UCSF Health, n.d.):
- Face the client with the hearing impairment directly when communicating.
- Refrain from talking while in another room or area away from the client.
- Do not shout; rather, speak slowly, clearly, and distinctly.
- Pause between concepts to ensure you are understood before continuing.
- If the hearing-impaired client does not seem to understand a word or phrase, rephrase the message.
- Avoid interrupting the client.
- Provide the client with written information such as a schedule and directions and ask them to repeat the specifics.


3.1.0: Vocabulario
In this module, we will learn how to describe our families as well as learn about other people’s families. Think about your family and how you would describe it in English.
Vocabulario
|
el padre |
father |
|---|---|
|
la madre |
mother |
|
el hermano |
brother |
|
la hermana |
sister |
|
el esposo |
husband |
|
la esposa |
wife |
|
la pareja |
partner |
|
el hijo |
son |
|
la hija |
daughter |
|
el padrastro |
stepfather |
|
la madrastra |
stepmother |
|
el hermanastro |
stepbrother |
|
la hermanastra |
stepdaughter |
|
el medio hermano |
half-brother |
|
la media hermana |
half-sister |
|
la mascota |
pet |
|
el tío |
uncle |
|---|---|
|
la tía |
aunt |
|
el sobrino |
nephew |
|
la sobrina |
niece |
|
el primo |
cousin m. |
|
la prima |
cousin f. |
|
el abuelo |
grandfather |
|
la abuela |
grandmother |
|
el suegro |
father-in-law |
|
la suegra |
mother-in-law |
|
el yerno |
son-in-law |
|
la nuera |
daughter-in-law |
|
el bisabuelo |
great grandfather |
|
la bisabuela |
great grandmother |
|
el hijo único |
only child/son |
|---|---|
|
la hija única |
only daughter |
|
(el/la) menor |
(youngest) younger |
|
(el/la) mayor |
(eldest) older |
|
los ancestros/los antepasados |
ancestors |
Use the following chat mat as you converse with others:


11.7: Negotiations
Learning OUTCOME
- Identify how a retailer can prepare for negotiations.
Let’s begin this discussion with a definition of the term negotiation :
A negotiation is a formal discussion between two or more parties to reach an agreement. [1]
As with many of the other topics we have discussed in this section, the principles of negotiation are the same for the retailer as they are for any business in general. Two obvious applications for negotiation are conflict management and procurement. These two examples illustrate the breadth of situations where negotiation skills need to be applied. Addressing personal conflict often involves emotional and cultural issues whereas procurement negotiation is usually about contractual terms and conditions.
Good Negotiator
Whatever the context, there are common factors that exemplify a good negotiator:
- the ability to describe common goals and boundaries;
- emotional control and equal treatment of all parties;
- good listening and communication skills;
- thorough knowledge of bargaining tactics;
- an ability to close a negotiation in a way that secures the outcome.
Negotiation Procedure
Regardless of whether the negotiation is competitive or collaborative, it usually follows a typical procedure:
- Plan: All parties should prepare thoroughly. This includes gathering as much information as possible; setting goals for the outcome and agreeing an escalation route if the negotiation is unsuccessful. Each party should attempt to understand the cultural, commercial and ethical background of the others.
- Discuss: Set the scene, identify the key issues and communicate the objectives. Listen, question and feedback regularly to confirm understanding.
- Propose: Propose a solution that is clear and unambiguous.
- Bargain: Discuss the proposal; communicate personal boundaries and areas of flexibility.
- Agree: Reach agreement on the core issues; document what has been agreed and record any peripheral, outstanding items with timescales for resolving them.
- Implement: Communicate the outcome of the negotiation as necessary, update management.
Negotiation is easy to get wrong. The cardinal sin is to enter into negotiations unprepared. This can easily lead to mistakes such as making opening offers that are clearly unacceptable to the other parties.
Specifically for a retailer, negotiations can be internally or externally focused. Internal negotiations typically are between departments. The merchandise buying office may negotiate for additional space for their product presentation with the store organization. The store organization may negotiate with the merchandise planning department for a larger allocation of certain goods.
External negotiations for retailers usually center around the procurement function of merchandise buyers. Typical buyer/vendor discussions would include issues like price, delivery, allocation, promotions, and allowances. Buyers should be thoroughly prepared with hard data regarding recent sales performance of the vendor’s products in their operation, actual product delivery versus contracted, markdowns taken by the retailer to clear goods, and any quality issues or returns.
Here is an excellent video from Margaret Neale from Stanford Graduate School of Business on some advanced negotiation skills.
Practice Questions
Contributors and Attributions
- Image: Negotiation Standoff. Provided by : Lumen Learning. License : CC BY: Attribution
- Negotiations. Provided by : Praxis. Located at : https://www.praxisframework.org/en/knowledge/negotiation . License : CC BY-SA: Attribution-ShareAlike
- Margaret Neale: Negotiation: Getting What You Want. Authored by : Stanford Graduate School of Business. Located at : https://youtu.be/MXFpOWDAhvM . License : All Rights Reserved . License Terms : Standard YouTube License


3.3: Formula for the Area of a Triangle
Lesson
Let's write and use a formula to find the area of a triangle.
Exercise \(\PageIndex{1}\): Bases and Heights of a Triangle
Study the examples and non-examples of bases and heights in a triangle.
- Examples: These dashed segments represent heights of the triangle.
- Non-examples: These dashed segments do not represent heights of the triangle.
Select all the statements that are true about bases and heights in a triangle.
- Any side of a triangle can be a base.
- There is only one possible height.
- A height is always one of the sides of a triangle.
- A height that corresponds to a base must be drawn at an acute angle to the base.
- A height that corresponds to a base must be drawn at a right angle to the base.
- Once we choose a base, there is only one segment that represents the corresponding height.
- A segment representing a height must go through a vertex.
Exercise \(\PageIndex{2}\): Finding a Formula for Area of a Triangle
For each triangle:
- Identify a base and a corresponding height, and record their lengths in the table.
- Find the area of the triangle and record it in the last column of the table.
| triangle | base (units) | height (units) | area (square units) |
|---|---|---|---|
| A | |||
| B | |||
| C | |||
| D | |||
| any triangle | \(b\) | \(h\) |
In the last row, write an expression for the area of any triangle, using \(b\) and \(h\).
Exercise \(\PageIndex{3}\): Applying the Formula for Area of Triangles
For each triangle, circle a base measurement that you can use to find the area of the triangle. Then, find the area of any three triangles. Show your reasoning.
Summary
- We can choose any of the three sides of a triangle to call the base . The term “base” refers to both the side and its length (the measurement).
- The corresponding height is the length of a perpendicular segment from the base to the vertex opposite of it. The opposite vertex is the vertex that is not an endpoint of the base.
Here are three pairs of bases and heights for the same triangle. The dashed segments in the diagrams represent heights.
A segment showing a height must be drawn at a right angle to the base, but it can be drawn in more than one place. It does not have to go through the opposite vertex, as long as it connects the base and a line that is parallel to the base and goes through the opposite vertex, as shown here.
The base-height pairs in a triangle are closely related to those in a parallelogram. Recall that two copies of a triangle can be composed into one or more parallelograms. Each parallelogram shares at least one base with the triangle.
For any base that they share, the corresponding height is also shared, as shown by the dashed segments.
We can use the base-height measurements and our knowledge of parallelograms to find the area of any triangle.
- The formula for the area of a parallelogram with base \(b\) and height \(h\) is \(b\cdot h\).
- A triangle takes up half of the area of a parallelogram with the same base and height. We can therefore express the area \(A\) of a triangle as: \(A=\frac{1}{2}\cdot b\cdot h\)
- The area of Triangle A is 15 square units because \(\frac{1}{2}\cdot 5\cdot 6=15\).
- The area of Triangle B is 4.5 square units because \(\frac{1}{2}\cdot 3\cdot 3=4.5\).
- The area of Triangle C is 24 square units because \(\frac{1}{2}\cdot 12\cdot 4=24\).
In each case, one side of the triangle is the base but neither of the other sides is the height. This is because the angle between them is not a right angle.
In right triangles, however, the two sides that are perpendicular can be a base and a height.
The area of this triangle is 18 square units whether we use 4 units or 9 units for the base.
Glossary Entries
Definition: Opposite Vertex
For each side of a triangle, there is one vertex that is not on that side. This is the opposite vertex.
For example, point \(A\) is the opposite vertex to side \(BC\).
Practice
Exercise \(\PageIndex{4}\)
Select all drawings in which a corresponding height \(h\) for a given base \(b\) is correctly identified.
- A
- B
- C
- D
- E
- F
Exercise \(\PageIndex{5}\)
For each triangle, a base and its corresponding height are labeled.
- Find the area of each triangle.
- How is the area related to the base and its corresponding height?
Exercise \(\PageIndex{6}\)
Here is a right triangle. Name a corresponding height for each base.
- Side \(d\)
- Side \(e\)
- Side \(f\)
Exercise \(\PageIndex{7}\)
Find the area of the shaded triangle. Show your reasoning.
(From Unit 1.3.2)
Exercise \(\PageIndex{8}\)
Andre drew a line connecting two opposite corners of a parallelogram. Select all true statements about the triangles created by the line Andre drew.
- Each triangle has two sides that are 3 units long.
- Each triangle has a side that is the same length as the diagonal line.
- Each triangle has one side that is 3 units long.
- When one triangle is placed on top of the other and their sides are aligned, we will see that one triangle is larger than the other.
- The two triangles have the same area as each other.
(From Unit 1.3.1)
Exercise \(\PageIndex{9}\)
Here is an octagon. (Note: The diagonal sides of the octagon are not 4 inches long.)
- While estimating the area of the octagon, Lin reasoned that it must be less than 100 square inches. Do you agree? Explain your reasoning.
- Find the exact area of the octagon. Show your reasoning.
(From Unit 1.1.3)


9.7C: Single-Stranded DNA Bacteriophages
- Illustrate the characteristics and life cycle of ssDNA bacteriophages
Nineteen viral families are currently recognized that infect bacteria and archaea. Of these, only two families have RNA genomes and only five are enveloped. Of the viral families with DNA genomes, only two have single-stranded genomes.
Inoviridae
The Inoviridae are a family of filamentous bacteriophages. The name of the family is derived from the Greek nos , meaning “muscle. ”
Taxonomy
There are two genera in this family: Inovirus and Plectrovirus. These genera differ in their host range: Plectovirii infect hosts of the class Mollicutes, while Inovirii infect species of the Enterobacteriaceae, Pseudomonadaceae, Spirillaceae, Xanthomonadaceae, Clostridium, and Propionibacterium classes.
Physical and Genomic Properties
Inoviridae are non-enveloped, rod-shaped, and filamentous. The capsid has a helical symmetry, and in general has a length of 85-280 nm or 760-1950 nm and a width of 10-16 nm or 6-8 nm, respectively. These morphological differences depend on the species.
The genomes are non-segmented, circular, positive-sense, single-stranded DNA, 4.4-8.5 kilobases in length. They encode 4 to 11 proteins. Replication of the genome occurs via a dsDNA intermediate and the rolling circle mechanism. Gene transcription is by the host’s cellular machinery, as each gene has a specific promoter.
Life Cycle
There are six steps in the life cycle of Inoviridae:
- Adsorbion to the host via specific receptor(s)
- Movement of the viral DNA into the host cell
- Conversion of the single-strand form to a double-stranded intermediate
- Replication of the viral genome
- Synthesis of the new virions
- Release of the new virions from the host
Action in Host
Conversion from single-stranded to double-stranded form is carried out by the host’s own DNA polymerase. The host’s RNA polymerase binds to the viral genome and syntheses RNA. Some of this RNA is translated and the remainder is used to initiate DNA replication.
Virion release may involve host lysis, but alternatively productive infection may occur by budding from the host membrane. This pattern is typically seen in the Plectivirus genus. A number of exceptions to this life cycle are known. Lysogenic species, which encode integrases, exist within this family.
Microviridae
The Microviridae are a family of bacteriophages with a single-stranded DNA genome. The name of this family is derived from the Greek micro , meaning “small. ” This refers to the size of their genomes, which are among the smallest of the DNA viruses.
Taxonomy
This family is divided into two subfamilies, Gokushovirinae (derived from the Japanese for “very small”) and Microvirinae. These groups differ in their hosts, genome structure, and virion composition.
Gokushoviruses are currently known to infect only obligate intra-cellular parasites. These species are members of the genera Bdellovibrio, Chlamydia, and Spiroplasma. Subfamily Microvirinae are all of the genus Microvirus. All seven such members infect Enterobacteria.
Physical and Genomic Properties
Members of the subfamily Gokushovirus have only two structural proteins: capsid proteins F (Virus Protein 1) and DNA pilot protein H (Virus Protein 2) and do not use scaffolding proteins. They also possess ‘mushroom-like’ protrusions positioned at the three-fold axes of symmetry of their icosahedral capsids. These are formed by large insertion loops within the protein F of gokushoviruses and are absent in the microviruses. They lack both the external scaffolding protein D and the major spike protein G of the species in the genus Microvirus. The genomes of this group tend to be smaller, about 4.5 kb in length. This subfamily includes the genera Bdellomicrovirus, Chlamydiamicrovirus, and Spiromicrovirus.
Microviridae are non-enveloped and round with an icosahedral symmetry. They have a diameter between 25-27 nanometers and lack tails. Each virion has 60 copies each of the F, G, and J proteins and 12 copies of the H protein. Viruses in this family replicate their genomes via a rolling circle mechanism and encode dedicated RCR initiation proteins. Although the majority of species in this family have lytic life cycles, a few may have temperate life cycles.
Life Cycle
There are a number of steps in the life cycle:
- Adsorbion to the host via specific receptor(s)
- Movement of the viral DNA into the host cell
- Conversion of the single-strand form to a double-stranded intermediate, known as the replicative form I
- Transcription of early genes
- Replication of the viral genome
- Late genes are now transcribed by the host’s RNA polymerase
- Synthesis of the new virions
- Maturation of the virions in the host cytoplasm
- Release from the host
Action in Host
Cell lysis is mediated by the phiX174-encoded protein E, which inhibits the peptidoglycan synthesis, leading to the eventual bursting of the infected cell.
Key Points
- The Inoviridae are a family of filamentous bacteriophages. The virons are non-enveloped, rod-shaped, and filamentous. Viron release may involve host lysis, but alternatively productive infection may occur by budding from the host membrane.
- The Microviridae are a family of bacteriophages with a single-stranded DNA genome. Their genomes are among the smallest of the DNA viruses. Although the majority of species in this family have lytic life cycles, a few may have temperate life cycles.
- The Microviridae are divided into two subfamilies, Gokushovirinae and Microvirinae. These groups differ in their hosts, genome structure, and viron composition.
Key Terms
- microviridae : The Microviridae are a family of bacteriophages with a single-stranded DNA genome.
- virion : A single individual particle of a virus (the viral equivalent of a cell).


3.7: Discussion Questions
How can ethics-based concepts such as truthfulness and fairness be integrated into the fabric of the organization?
2 .How can we nurture an environment where each member of the organization develops and internalizes a moral compass?
3 .Evaluate how an entrepreneurial business startup might benefit from the enforcement of antitrust laws against a large competitor.
4 .Discuss ways in which intellectual property, such as trademarks, can add value to a small business. How would you protect your ability to monetize intellectual property?
5 .In this section of the chapter, there is an example of a customer data breach via computer hacking. Discuss the biggest risks of storing customer or company information online. What are some of the steps you would take to prevent a data breach?
6 .Can a social enterprise work on a social issue and at the same time be profitable?
7 .How will you ensure that your organization learns to develop and deliver products and services that reduces your carbon footprint?
8 .Referring to Table 3.3 listing cases of corporate fraud, which company example do you think is one of the worst examples of unethical conduct? Is this because it involved the most money stolen, the most people cheated, or the most devious methods?
9 .If an entrepreneur values sustainability and environmental awareness, does that mean the bottom line will suffer? Alternatively, is there a way to protect the environment and still make a profit?
10 .You have learned about B-corporations. If you started a new business, would you commit to the rather stringent audit process necessary to become a B-corporation? Why or why not?
11 .How can an entrepreneur maximize the benefits of a diverse workforce to develop a competitive advantage?
12 .How can you combat the negative impact of biases and prejudices in your organization?
13 .What would you do, as an entrepreneur, to make your employees feel you value their input and that they are free to speak honestly?
14 .Explain why diversity is something that should matter to an owner. What would you do to try to achieve it?
15 .Some small entrepreneurs do not have the budget for a full-fledged human resources department; however, that makes compliance with employment laws challenging. What steps would you take to comply with federal and state employment law if you do not have a full-time attorney or human resources specialist on staff?


10.4E: Exercises
Section 10.3 Exercises
Practice Makes Perfect
In the following exercises, convert from exponential to logarithmic form.
- \(4^{2}=16\)
- \(2^{5}=32\)
- \(3^{3}=27\)
- \(5^{3}=125\)
- \(10^{3}=1000\)
- \(10^{-2}=\frac{1}{100}\)
- \(x^{\frac{1}{2}}=\sqrt{3}\)
- \(x^{\frac{1}{3}}=\sqrt[3]{6}\)
- \(32^{x}=\sqrt[4]{32}\)
- \(17^{x}=\sqrt[5]{17}\)
- \(\left(\frac{1}{4}\right)^{2}=\frac{1}{16}\)
- \(\left(\frac{1}{3}\right)^{4}=\frac{1}{81}\)
- \(3^{-2}=\frac{1}{9}\)
- \(4^{-3}=\frac{1}{64}\)
- \(e^{x}=6\)
- \(e^{3}=x\)
- Answer
-
2. \(\log _{2} 32=5\)
4. \(\log _{5} 125=3\)
6. \(\log \frac{1}{100}=-2\)
8. \(\log _{x} \sqrt[3]{6}=\frac{1}{3}\)
10. \(\log _{17} \sqrt[5]{17}=x\)
12. \(\log _{\frac{1}{3}} \frac{1}{81}=4\)
14. \(\log _{4} \frac{1}{64}=-3\)
16. \(\ln x=3\)
In the following exercises, convert each logarithmic equation to exponential form.
- \(3=\log _{4} 64\)
- \(6=\log _{2} 64\)
- \(4=\log _{x} 81\)
- \(5=\log _{x} 32\)
- \(0=\log _{12} 1\)
- \(0=\log _{7} 1\)
- \(1=\log _{3} 3\)
- \(1=\log _{9} 9\)
- \(-4=\log _{10} \frac{1}{10,000}\)
- \(3=\log _{10} 1,000\)
- \(5=\log _{e} x\)
- \(x=\log _{e} 43\)
- Answer
-
2. \(64=2^{6}\)
4. \(32=x^{5}\)
6. \(1=7^{0}\)
8. \(9=9^{1}\)
10. \(1,000=10^{3}\)
12. \(43=e^{x}\)
In the following exercises, find the value of \(x\) in each logarithmic equation.
- \(\log _{x} 49=2\)
- \(\log _{x} 121=2\)
- \(\log _{x} 27=3\)
- \(\log _{x} 64=3\)
- \(\log _{3} x=4\)
- \(\log _{5} x=3\)
- \(\log _{2} x=-6\)
- \(\log _{3} x=-5\)
- \(\log _{\frac{1}{4}} \frac{1}{16}=x\)
- \(\log _{\frac{1}{3}} \frac{1}{9}=x\)
- \(\log _{\frac{1}{4}} 64=x\)
- \(\log _{\frac{1}{9}} 81=x\)
- Answer
-
2. \(x=11\)
4. \(x=4\)
6. \(x=125\)
8. \(x=\frac{1}{243}\)
10. \(x=2\)
12. \(x=-2\)
In the following exercises, find the exact value of each logarithm without using a calculator.
- \(\log _{7} 49\)
- \(\log _{6} 36\)
- \(\log _{4} 1\)
- \(\log _{5} 1\)
- \(\log _{16} 4\)
- \(\log _{27} 3\)
- \(\log _{\frac{1}{2}} 2\)
- \(\log _{\frac{1}{2}} 4\)
- \(\log _{2} \frac{1}{16}\)
- \(\log _{3} \frac{1}{27}\)
- \(\log _{4} \frac{1}{16}\)
- \(\log _{9} \frac{1}{81}\)
- Answer
-
2. \(2\)
4. \(0\)
6. \(\frac{1}{3}\)
8. \(-2\)
10. \(-3\)
12. \(-2\)
In the following exercises, graph each logarithmic function.
- \(y=\log _{2} x\)
- \(y=\log _{4} x\)
- \(y=\log _{6} x\)
- \(y=\log _{7} x\)
- \(y=\log _{1.5} x\)
- \(y=\log _{2.5} x\)
- \(y=\log _{\frac{1}{3}} x\)
- \(y=\log _{\frac{1}{5}} x\)
- \(y=\log _{0.4} x\)
- \(y=\log _{0.6} x\)
- Answer
-
2.
4.
6.
8.
10.
In the following exercises, solve each logarithmic equation.
- \(\log _{a} 16=2\)
- \(\log _{a} 81=2\)
- \(\log _{a} 8=3\)
- \(\log _{a} 27=3\)
- \(\log _{a} 32=2\)
- \(\log _{a} 24=3\)
- \(\ln x=5\)
- \(\ln x=4\)
- \(\log _{2}(5 x+1)=4\)
- \(\log _{2}(6 x+2)=5\)
- \(\log _{3}(4 x-3)=2\)
- \(\log _{3}(5 x-4)=4\)
- \(\log _{4}(5 x+6)=3\)
- \(\log _{4}(3 x-2)=2\)
- \(\ln e^{4 x}=8\)
- \(\ln e^{2 x}=6\)
- \(\log x^{2}=2\)
- \(\log \left(x^{2}-25\right)=2\)
- \(\log _{2}\left(x^{2}-4\right)=5\)
- \(\log _{3}\left(x^{2}+2\right)=3\)
- Answer
-
2. \(a=9\)
4. \(a=3\)
6. \(a=\sqrt[3]{24}\)
8. \(x=e^{4}\)
10. \(x=5\)
12. \(x=17\)
14. \(x=6\)
16. \(x=3\)
18. \(x=-5 \sqrt{5}, x=5 \sqrt{5}\)
20. \(x=-5, x=5\)
In the following exercises, use a logarithmic model to solve.
- What is the decibel level of normal conversation with intensity \(10^{−6}\) watts per square inch?
- What is the decibel level of a whisper with intensity \(10^{−10}\) watts per square inch?
- What is the decibel level of the noise from a motorcycle with intensity \(10^{−2}\) watts per square inch?
- What is the decibel level of the sound of a garbage disposal with intensity \(10^{−2}\) watts per square inch?
- In 2014, Chile experienced an intense earthquake with a magnitude of \(8.2\) on the Richter scale. In 2010, Haiti also experienced an intense earthquake which measured \(7.0\) on the Richter scale. Compare the intensities of the two earthquakes.
- The Los Angeles area experiences many earthquakes. In 1994, the Northridge earthquake measured magnitude of \(6.7\) on the Richter scale. In 2014, Los Angeles also experienced an earthquake which measured \(5.1\) on the Richter scale. Compare the intensities of the two earthquakes.
- Answer
-
2. A whisper has a decibel level of \(20\) dB.
4. The sound of a garbage disposal has a decibel level of \(100\) dB.
6. The intensity of the 1994 Northridge earthquake in the Los Angeles area was about \(40\) times the intensity of the 2014 earthquake.
- Explain how to change an equation from logarithmic form to exponential form.
- Explain the difference between common logarithms and natural logarithms.
- Explain why \(\log _{a} a^{x}=x\).
- Explain how to find the \(\log _{7} 32\) on your calculator.
- Answer
-
2. Answers may vary
4. Answers may vary
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all objectives?


1: Essential Ideas of Chemistry
Most everything you do and encounter during your day involves chemistry. Making coffee, cooking eggs, and toasting bread involve chemistry. The products you use—like soap and shampoo, the fabrics you wear, the electronics that keep you connected to your world, the gasoline that propels your car—all of these and more involve chemical substances and processes. Whether you are aware or not, chemistry is part of your everyday world. In this course, you will learn many of the essential principles underlying the chemistry of modern-day life.
Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


14.2: Word Components Related To The Muscular System
This section will describe common word components related to the muscular system. These word components help build definitions for many medical terms. Other common prefixes are described in Chapter 1.3 , and common suffixes are described in Chapter 1.5.
Prefixes Related to the Muscular System
- a- : Absence of, without
- ab- : Away from
- ad- : Towards
- brady- : Slow
- dys- : Painful, difficult, abnormal, labored
- hyper- : Above, excessive
- inter- : Between
- intra- : Within, in
- poly- : Many, much
- sub- : Below, under
- supra- : Above
- sym- : Together, joined
- syn- : Together, joined
Word Roots With a Combining Vowel Related to the Muscular System
- ankyl /o: Stiff or bent
- electr /o: Electricity; electrical activity
- fasci /o: Fascia
- fibr /o: Fibrous connective tissue
- kinesi /o: Movement, motion
- kyph /o: Hump
- lamin /o: Lamina (thin, flat plate or layer)
- leimy /o: Smooth (visceral)muscle that lines the walls of internal organs
- my /o: Muscle
- myel /o: Spinal cord, bone marrow
- myos /o: Muscle
- myocardi /o: Heart muscle
- plant /o: Sole of the foot
- rhabd /o: Rod-shaped, striated
- sarc /o: Flesh, connective tissue
- ten /o: Tendon
- tend /o: Tendon
- tendin /o: Tendon
Suffixes Related to the Muscular System
- -ad : Toward
- -al : Pertaining to
- -algia : Pain
- -ar : Pertaining to
- -asthenia : Weakness
- -centesis : Surgical puncture to aspirate fluid
- -desis : Surgical fixation, fusion
- -ectomy : Excision, surgical removal, cutting out
- -gram : The record, radiographic image
- -graphy : Process of recording, radiographic imaging
- -ic : Pertaining to
- -itis : Inflammation
- -lysis : Loosening, separating, dissolution
- -oid : Resembling
- -oma : Tumor
- -osis : Abnormal condition
- -penia : Abnormal reduction
- -physis : Growth
- -plasty : Surgical repair
- -rrhaphy : Suturing, repairing
- -sarcoma : Malignant tumor
- -schisis : Split, fissure
- -scopy : Process of viewing, visual examination
- -tome : Instrument used to cut
- -tomy : Incision, cut into
- -trophy : Nourishment, development