Evaluating Logarithms

To write the given equation in logarithmic form, we should recall the definition of a logarithm. $$\begin{array}{c}x=b^y\iff {\log }_b(x)=y\end{array}$$ The above relationship tells us that the logarithm $y$ is the exponent to which $b$ must be raised to get $x.$ Let's now apply the definition to the given equation. $$\begin{array}{c}{5}^{\text{-}2}=\frac{1}{25}\iff {\log }_5\left(\frac{1}{25}\right)=\text{-}2\end{array}$$ The above means that $\text{-}2$ is the exponent to which $5$ must be raised to obtain $\frac{1}{25}.$