Difference between revisions of "2015 AMC 12A Problems/Problem 14"
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Revision as of 22:32, 4 February 2015
Problem 14
What is the value of for which
?
$\textbf{(A)}\ 9\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}}\ 24\qquad\textbf{(E)}\ 36$ (Error compiling LaTeX. Unknown error_msg)
Solution
We use the change of base formula to show that
Thus, our equation becomes
which becomes after combining:
Hence
, and the answer is