Answer
$log_8{2}=\frac{1}{3}$
Work Step by Step
From the definition of the logarithmic function on page 456, we know that $b^{y}=x$ is equivalent to $y=log_b{x}$ (for $x\gt0$, $b\gt0$, and $b\ne1$).
Therefore, $\sqrt[3] 8=2(=8^{\frac{1}{3}})$ is equivalent to $log_8{2}=\frac{1}{3}$ in logarithmic form.