2007 AMC 12A 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}\qquad \mathrm{(B)}\ \sqrt {3}\qquad \mathrm{(C)}\ \sqrt [3]{6}\qquad \mathrm{(D)}\ \sqrt {6}\qquad \mathrm{(E)}\ 6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.