# How do you solve 5^x=45?

Oct 17, 2016

$x = 2.365$

#### Explanation:

${5}^{x} = 45$

$\log {5}^{x} = \log 45 \textcolor{w h i t e}{a a a}$Take the log of both sides

$x \log 5 = \log 45 \textcolor{w h i t e}{a a a}$Use the log rule $\log {x}^{a} = a \log x$

$\frac{x \log 5}{\log} 5 = \log \frac{45}{\log} 5 \textcolor{w h i t e}{a a a}$Divide both sides by log5

$x = 2.365$