# Problem #1789

 1789 Let $m>1$ and $n>1$ be integers. Suppose that the product of the solutions for $x$ of the equation $$8(\log_n x)(\log_m x)-7\log_n x-6 \log_m x-2013 = 0$$ is the smallest possible integer. What is $m+n$? $\textbf{(A)}\ 12\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 272$ This problem is copyrighted by the American Mathematics Competitions.
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