Answer
$\left\{\dfrac{1}{36}\right\}$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, then the given equation, $
\log_6x=-2
$, implies
\begin{align*}\require{cancel}
x&=6^{-2}
\\\\
x&=\dfrac{1}{6^2}
&(\text{use }a^{-m}=\dfrac{1}{a^m})
\\\\
x&=\dfrac{1}{36}
.\end{align*}
Hence, the solution set of $
\log_6x=-2
$ is $\left\{\dfrac{1}{36}\right\}$.
