Answer
$x=-2$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{6}6^{-2}=x$ is equivalent to $6^{x}=6^{-2}$.
Therefore, $x=-2$, because $6^{-2}=6^{-2}$.
