# How do you solve 5^(2x) = 8?

May 13, 2016

$x = \textcolor{b l u e}{\frac{{\log}_{5} 8}{2}} \approx \textcolor{b l u e}{0.646}$

#### Explanation:

If ${5}^{2 x} = 8$
then
$\textcolor{w h i t e}{\text{XXX}} {\log}_{5} {5}^{2 x} = {\log}_{5} 8$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 2 x = {\log}_{5} 8$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = \frac{{\log}_{5} 8}{2}$

Use a calculator to obtain an approximate value for this expression.