If $\log_2(\log_3(\log_4 x))=\log_3(\log_4(\log_2 y))=\log_4(\log_2(\log_3 z))=0$, then the sum $x+y+z$ is equal to
$\textbf{(A) }50\qquad \textbf{(B) }58\qquad \textbf{(C) }89\qquad \textbf{(D) }111\qquad  \textbf{(E) }1296$
If $\log_{x}{n}=0,$ then $n = 1.$ So, we can rewrite this equation:
\[(\log_3(\log_4 x))=(\log_4(\log_2 y))=(\log_2(\log_3 z))=1\]
Solve individually for each variable.
\[x = 4^3 = 64\]
\[y = 2^4 = 16\]
\[z = 3^2 = 9\]
Therefore, $x + y + z = 89.$
The answer is $\textbf{(C)}.$
-edited by coolmath34