#### Answer

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

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