# What is an example of an exponential equation and its related logarithmic equation?

Nov 13, 2016

$625 = {5}^{4} \mathmr{and} 4 = {\log}_{5} 625$
$100000 = {19}^{5} \mathmr{and} 5 = \log 100000$
$1 = {e}^{0} \mathmr{and} 0 = \ln 1$

#### Explanation:

$y = {b}^{x}$ is called an exponential equation and its inverse

$x = {\log}_{b} y$ is called a logarithmic equation.

Examples:

$625 = {5}^{4} \mathmr{and} 4 = {\log}_{5} 625$

$100000 = {19}^{5} \mathmr{and} 5 = \log 100000$

$1 = {e}^{0} \mathmr{and} 0 = \ln 1$