Problem 422

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Problem 422: (2007 AMC 12A, 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$

Solution

Exercise 422: Solution

Square $ABCD$ has area $4,$ 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 $a?$

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