8.35 If the following equation holds
$$
\log _{2}\left[\log _{3}\left(\log _{4} x\right)\right]=\log _{3}\left[\log _{4}\left(\log _{2} y\right)\right]=\log _{4}\left[\log _{2}\left(\log _{3} z\right)\right]=0 \text {, }
$$

then the sum $x+y+z$ is equal to
(A) 50.
(B) 58.
(C) 89.
(D) 111.
(E) 1296.
(22nd American High School Mathematics Examination, 1971)
[Solution] If $\log _{a} b=0$, then $b=1$.
So $\log _{3}\left(\log _{4} x\right)=\log _{4}\left(\log _{2} y\right)=\log _{2}\left(\log _{3} z\right)=1$.
Therefore $\log _{4} x=3, \log _{2} y=4, \log _{3} z=2$.
$$
\therefore \quad x+y+z=4^{3}+2^{4}+3^{2}=89 \text {. }
$$

Therefore, the answer is $(C)$.