11. Suppose that $\log _{2}\left[\log _{3}\left(\log _{4} a\right)\right]-\log _{3}\left[\log _{4}\left(\log _{2} b\right)\right]=\log _{4}\left[\log _{2}\left(\log _{3} c\right)\right]=0$. Find the value of $a+b+c$.
11. Answer: 89 $\log _{2}\left[\log _{3}\left(\log _{4} a\right)\right]=0$ implies $\log _{3}\left(\log _{4} a\right)-1$. Hence $\log _{4} a=3$, hence $a=64$. Similarly, $b=16$ and $c=9$. Therefore $a+b+c=89$.