AMC 12 2015a Problem 14

What is the value of $a$ for which $\frac{1}{\log_2 a} + \frac{1}{\log_3 a} + \frac{1}{\log_4 a} = 1$?

\textbf{(A)}\ 9 \textbf{(B)}\ 12 \textbf{(C)}\ 18 \textbf{(D)}\ 24 \textbf{(E)}\ 36