Answer
$log_{10}\frac{1}{100}=-2$
Work Step by Step
We are given $10^{-2}=\frac{1}{100}$.
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x$ and every real number $y$.
Therefore, $10^{-2}=\frac{1}{100}$ is equivalent to $log_{10}\frac{1}{100}=-2$.
