# How do you solve 5^(2x)=20?

May 4, 2018

The solution is $x = {\log}_{5} \frac{20}{2}$.

#### Explanation:

To solve the equation, take the ${\log}_{5}$ of both sides:

${5}^{2 x} = 20$

${\log}_{5} \left({5}^{2 x}\right) = {\log}_{5} \left(20\right)$

$\textcolor{red}{\cancel{\textcolor{b l a c k}{{\log}_{5}}}} \left({\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}^{2 x}\right) = {\log}_{5} \left(20\right)$

$2 x = {\log}_{5} \left(20\right)$

$x = {\log}_{5} \frac{20}{2}$

$\textcolor{w h i t e}{x} \approx 0.930677 \ldots$

Hope this helped!