Answer
$\log_{1/10} 1000=-3$
Work Step by Step
Since $y=b^x$ is equivalent to $\log_b y=x,$ then the given equation, $
\left( \dfrac{1}{10} \right)^{-3}=1000
,$ is equivalent to
\begin{array}{l}\require{cancel}
\log_{1/10} 1000=-3
.\end{array}