Answer
$x=\pm5$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_6(x^2+11)=2
$, implies
\begin{align*}\require{cancel}
x^2+11&=6^2
\\
x^2+11&=36
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
x^2&=36-11
\\
x^2&=25
.\end{align*}
Taking the square root of both sides, the equation above is equivalent to
\begin{align*}\require{cancel}
x&=\pm\sqrt{25}
\\
x&=\pm5
.\end{align*}
Hence, the solution to the equation $
\log_6(x^2+11)=2
$ is $
x=\pm5
$.
