Answer
$x=\frac{log(7)}{2log(3)}\approx.8856$
Work Step by Step
According to the logarithm property of equality $log_{b}a=log_{b}c$ is equivalent to $a=c$ (where a, b, and c are real numbers such that $log_{b}a$ and $log_{b}c$ are real numbers and $b\ne1$). We can use this property to solve for x.
$3^{2x}=7$
Take the common logarithm of both sides (which has base 10).
$log(3^{2x})=log(7)$
Use the power property of logarithms.
$2x log(3)=log(7)$
Divide both sides by $2log(3)$.
$x=\frac{log(7)}{2log(3)}\approx.8856$
