Question

In the following exercises, convert from exponential to logarithmic form.

${63}^{\frac{1}{5}}=\sqrt[5]{63}$.

Short answer

The logarithmic form is

${\log }_{63}\left(\sqrt[5]{63}\right)=\frac{1}{5}$.

Step-by-step solution

Step 1. Given information.

The given expression is

${63}^{\frac{1}{5}}=\sqrt[5]{63}$.

Step 2. Converting into the logarithmic form.

$$\begin{gathered} {63}^{\frac{1}{5}}=\sqrt[5]{63} \\ {a}^y=x \\ {\log }_a\left(x\right)=y \\ {\log }_{63}\left(\sqrt[5]{63}\right)=\frac{1}{5} \end{gathered}$$

Therefore, the logarithmic form is

${\log }_{63}\left(\sqrt[5]{63}\right)=\frac{1}{5}$.