# What is a logarithm?

Oct 15, 2014

The logarithm base $b$ of a number $n$ is the number $x$ that when $b$ is raised to $x$th power, the resulting value is $n$

${\log}_{b} n = x \iff {b}^{x} = n$

Example:

${\log}_{2} 8 = x$

$\implies {2}^{x} = 8$
$\implies {2}^{x} = {2}^{3}$
$\implies x = 3$

${\log}_{5} 1 = x$
$\implies {5}^{x} = 1$
$\implies {5}^{x} = {5}^{0}$
$\implies x = 0$