Answer
$x=9$
Work Step by Step
Since $y=b^x$ is equivalent to $\log_b y=x$, then the given equation, $
\log_3 x^2=4
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2=3^4
.\end{array}
Using concepts of quadratic equations, the solutions to the equation above are
\begin{array}{l}\require{cancel}
x^2=81
\\\\
x=\pm\sqrt{81}
\\\\
x=\pm\sqrt{(9)^2}
\\\\
x=\pm9
.\end{array}
Upon checking, only $
x=9
$ satisfies the original equation.
