The solution to the equation \log _{3 x} 4=\log _{2 x} 8, where x is a positive real number other than \dfrac{1}{3} or \dfrac{1}{2}, can be written as \dfrac{p}{q}, where p and q are relatively prime positive integers. What is p+q ?
Answer Choices
A. 5
B. 13
C. 17
D. 31
E. 35