One of the greatest strengths of behavioral psychology is the ability to clearly observe and measure behaviors. Weaknesses of this approach include failing to address cognitive and biological processes that influence human actions.
Right away we see that expressions (a), (b), and (d) are equivalent, since addition is commutative: $2x + 8 = 8 + 2x$. We now only have to check (c) and (e). If $x=0$, (c) and (e) have the value 4, whereas (a), (b), and (d) have the value 8.So (c) and (e) are not equivalent to (a), (b), and (d).Moreover, if $x=1$, then (c) has the value 6 and (e) has the value 5, so those two expressions are not equivalent either.For (c), we can use the distributive property and decompose one of the numbers to write two equivalent expressions: $$ \begin{align} &2x+4 \\ &2(x+2) \\ &2(x+1+1) \end{align} $$.o (c) and (e) are not equivalent to (a), (b), and (d). Moreover, if $x=1$, then (c) has the value 6 and (e) has the value 5, so those two expressions are not equivalent either. For (c), we can use the distributive property and decompose one of the numbers to write two equivalent expressions:
In the example above, the equation log4(x + 1) + log4(x + 1) / 2 = log4(8) can be simplified to log4(x + 1) + log4(x + 1)^(1/2) = log4(8), using the power rule for logarithms. By using the product rule for logarithms, the equation can be further simplified to log4(x + 1)(x + 1)^(1/2) = log4(8). Eliminate the logarithm.By taking both sides of the equation to the power of 4, the example equation simplifies to (x + 1)(x + 1)^(1/2) = 8, which further simplifies to (x + 1)^(3/2) = 8. Solve for x. In the example above, this is done by taking both sides of the equation to the power of 2/3.liminate the logarithm. By taking both sides of the equation to the power of 4, the example equation simplifies to (x + 1)(x + 1)^(1/2) = 8, which further simplifies to (x + 1)^(3/2) = 8. Solve for x. In the example above, this is done by taking both sides of the equation to the power of 2/3.