Chapter 12 - Exponential Functions and Logarithmic Functions - 12.3 Logarithmic Functions - 12.3 Exercise Set - Page 803: 90

$x=4$

Converting to exponential form, the solution to the given logarithmic equation, $ \log_{8}{x}=\dfrac{2}{3} ,$ is \begin{array}{l}\require{cancel} x=8^{2/3} \\\\ x=\left( \sqrt[3]{8} \right)^2 \\\\ x=\left( 2 \right)^2 \\\\ x=4 .\end{array}