Answer
-3
Work Step by Step
We know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (where $x\gt0$, $b\gt0$, and $b\ne1$).
Also, based on the definition of the common logarithm, we know that $log(x)=log_{10}x$.
Therefore, $log(\frac{1}{1000})=log_{10}\frac{1}{1000}=-3$, because $10^{-3}=\frac{1}{10^{3}}=\frac{1}{1000}$.
