Evaluating Logarithms

To write the given equation in exponential form, we will recall the definition of a logarithm. $$\begin{array}{c}{\log }_b(x)=y\iff x=b^y\end{array}$$ This means that $y$ is the exponent to which $b$ must be raised to get $x.$ In our exercise, $\text{-}3$ is the exponent to which $3$ must be raised to get $\frac{1}{27}.$ $$\begin{array}{c}{\log }_3\left(\frac{1}{27}\right)=\text{-}3\iff \frac{1}{27}=3^{\text{-}3}\end{array}$$