Answer
-1
Work Step by Step
For any positive real number $b$ (such that $b\ne1$), we know that $log_{b}b^{r}=r$ (as long as $r\gt0$).
For $log_{6}\frac{1}{6}$:
We know that $6^{-1}=\frac{1}{6}$, so we can replace $\frac{1}{6}$ with $6^{-1}$.
Therefore, $log_{6}\frac{1}{6}=log_{6}6^{-1}=-1$.
