Here is another way to look at it.
$\displaystyle x = {\log _8}(4)\; \Rightarrow {8^x} = 4\; \Rightarrow \;x = \frac{2}{3}$.
That is correct but it might not be immediately apparent to dan713 that x = 2/3. Unless you note that $\displaystyle \sqrt[3]{8^2} = 4$, or you write it as $\displaystyle 2^{3x} = 2^2$.