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. $$\begin{array}{c}{6}^{\text{-}3}=\frac{1}{216}\iff {\log }_6\left(\frac{1}{216}\right)=\text{-}3\end{array}$$ The above means that $\text{-}3$ is the exponent to which $6$ must be raised to obtain $\frac{1}{216}.$