section_path: Motivation
section_name: Motivation
paragraph_text: Motivation
  
  Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations. The inverse of addition is subtraction, and the inverse of multiplication is division. Similarly, a logarithm is the inverse operation of exponentiation. Exponentiation is when a number b, the base, is raised to a certain power y, the exponent, to give a value x; this is denoted b y = x. {\displaystyle b^{y}=x.} For example, raising 2 to the power of 3 gives 8: 2 3 = 8. {\displaystyle 2^{3}=8.}
  
  The logarithm of base b is the inverse operation, that provides the output y from the input x. That is, y = log b x {\displaystyle y=\log _{b}x} is equivalent to x = b y {\displaystyle x=b^{y}} if b is a positive real number. (If b is not a positive real number, both exponentiation and logarithm can be defined but may take several values, which makes definitions much more complicated.)
  
  One of the main historical motivations of introducing logarithms is the formula log b (x y) = log b x + log b y, {\displaystyle \log _{b}(xy)=\log _{b}x+\log _{b}y,} by which tables of logarithms allow multiplication and division to be reduced to addition and subtraction, a great aid to calculations before the invention of computers.