# How do you solve for x in (125)^x = 625?

Apr 9, 2016

$x = \frac{4}{3} = 1.333$

#### Explanation:

${125}^{x} = 625$ means $x = {\log}_{125} 625$

As ${\log}_{b} a = \log \frac{a}{\log} b$

$x = \log \frac{625}{\log} 125 = \frac{2.79588}{2.09691} = 1.333$

Alternately - ${125}^{x} = 625 \Leftrightarrow {\left({5}^{3}\right)}^{x} = {5}^{4} \Leftrightarrow {5}^{3 x} = {5}^{4}$ or

$3 x \log 5 = 4 \log 5$ or $x = \frac{4}{3} = 1.333$