AMC 12 2018a Problem 14

The solution to the equation $\log_{3x} 4 = \log_{2x} 8$, where $x$ is a positive real number other than $\frac{1}{3}$ or $\frac{1}{2}$, can be written as $\frac {p}{q}$ where $p$ and $q$ are relatively prime positive integers. What is $p + q$?

$\textbf{(A) } 5 \textbf{(B) } 13 \textbf{(C) } 17 \textbf{(D) } 31 \textbf{(E) } 35$