# How do you solve 2log_5x=log_5 9?

##### 1 Answer
Oct 15, 2016

$x = 3$

#### Explanation:

Remember the general relation:
$\textcolor{w h i t e}{\text{XXX}} {\log}_{b} \left({a}^{c}\right) = c \cdot {\log}_{b} \left(a\right)$

Therefore
$\textcolor{w h i t e}{\text{XXX}} 2 {\log}_{5} \left(x\right) = {\log}_{5} \left({x}^{2}\right) = {\log}_{5} \left(9\right)$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {x}^{2} = 9$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 3$ (since the argument of $\log$ can not be negative)