#### Answer

$log_{10}\frac{1}{100}=-2$

#### 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, $10^{-2}=\frac{1}{100}$ can be written as the logarithmic equation $log_{10}\frac{1}{100}=-2$.