Question 22
Let $m \gt 1$ and $n \gt 1$ be integers. Suppose that the product of the solutions for $x$ of the equation
$$
\begin{aligned} &8(\log_n x)(\log_m x) - 7\log_n x \\ &\quad {}- 6\log_m x - 2013 = 0 \end{aligned}
$$
is the smallest possible integer. What is $m + n?$
$$
\begin{aligned} &8(\log_n x)(\log_m x) - 7\log_n x \\ &\quad {}- 6\log_m x - 2013 = 0 \end{aligned}
$$
is the smallest possible integer. What is $m + n?$