#### Answer

$log_5{\frac{1}{125}}=-3$

#### Work Step by Step

From the definition of the logarithmic function on page 456, we know that $b^{y}=x$ is equivalent to $y=log_b{x}$ (for $x\gt0$, $b\gt0$, and $b\ne1$).
Therefore, $5^{-3}=\frac{1}{125}$ is equivalent to $log_5{\frac{1}{125}}=-3$ in logarithmic form.