Glossary (Version 8.4)

The logarithm of a positive number x is the power to which a given number b, called the base, must be raised in order to produce the number x. The logarithm of x, to the base b is denoted by \(\;\log_bx\).

Algebraically, the statements \(\log_bx=y\) and \(b^y=x\) are equivalent in the sense that both statements express the identical relationship between x, y and b. For example, \(\log_{10}\;100=2\) because \(10^2=100,\), and \(\log_2\left(\frac1{32}\right)=-5\) because \(2^{-5}=\frac1{32}\).