Question

Convert from exponential to logarithmic form:

${32}^x=\sqrt[4]{32}$.

Short answer

The logarithmic form is,

$x={\log }_{32}\left(\sqrt[4]{32}\right)$.

Step-by-step solution

Step 1. Given the information.

The exponential form is,

${32}^x=\sqrt[4]{32}$.

Step 2. Converting to logarithmic form.

$$\begin{gathered} {32}^x=\sqrt[4]{32} \\ y={\log }_a\left(x\right) \\ x={\log }_{32}\left(\sqrt[4]{32}\right) \end{gathered}$$

If ${32}^x=\sqrt[4]{32}$,

then$x={\log }_{32}\left(\sqrt[4]{32}\right)$.