Answer
$x=8$
Work Step by Step
Since $y=b^x$ is equivalent to $\log_b y=x$, then the given equation, $
\log_2 x^2=6
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2=2^6
.\end{array}
Using concepts of quadratic equations, the solutions to the equation above are
\begin{array}{l}\require{cancel}
x^2=64
\\\\
x=\pm\sqrt{64}
\\\\
x=\pm\sqrt{(8)^2}
\\\\
x=\pm8
.\end{array}
Upon checking, only $
x=8
$ satisfies the original equation.
