Answer
$x=16$
Work Step by Step
From the definition of the logarithmic function on page 456, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$, $b\gt0$, and $b\ne1$).
Therefore, $log_{64}x=\frac{2}{3}$ is equivalent to $64^{\frac{2}{3}}=x$ in logarithmic form.
We know that $64^{\frac{2}{3}}=\sqrt[3] 64^{2}=(\sqrt[3] 64)^{2}=(4)^{2}=16$. So, $x=16$.
