AMC 12 2007a Problem 23

Square $ABCD$ has area $36,$ and $\overline{AB}$ is parallel to the x-axis. Vertices $A,$ $B$, and $C$ are on the graphs of $y = \log_{a}x,$ $y = 2\log_{a}x,$ and $y = 3\log_{a}x,$ respectively. What is $a?$

$\mathrm{(A)}\ \sqrt [6]{3} \mathrm{(B)}\ \sqrt {3} \mathrm{(C)}\ \sqrt [3]{6} \mathrm{(D)}\ \sqrt {6} \mathrm{(E)}\ 6$