Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 89

$x=4$

Converting to exponential form, the solution to the given logarithmic equation, $ \log_{32}{x}=\dfrac{2}{5} ,$ is \begin{array}{l}\require{cancel} \\\\ x=32^{2/5} \\\\ x=\left( \sqrt[5]{32} \right)^2 \\\\ x=\left( 2 \right)^2 \\\\ x=4 .\end{array}