Chapter 4 - Summary, Review, and Test - Review Exercises - Page 510: 29

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We know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (where $x\gt0$, $b\gt0$, and $b\ne1$). Therefore, $log_{3}(log_{8}8)=log_{3}1=0$. We know that $log_{8}8=1$, because $8^{1}=8$. We know that $log_{3}1=0$, because $3^{0}=1$.