AHSME 1960 Problem 24

If $\log_{2x}216 = x$, where $x$ is real, then $x$ is: $\textbf{(A)}\ \text{A non-square, non-cube integer}$ $\textbf{(B)}\ \text{A non-square, non-cube, non-integral rational number}$ $\textbf{(C)}\ \text{An irrational number}$ $\textbf{(D)}\ \text{A perfect square}$ $\textbf{(E)}\ \text{A perfect cube}$