MathDB
Wooden logs?

Source: 2018 AMC 12A #14

February 8, 2018
AMCAMC 12AMC 12 Anumber theorylogarithms

Problem Statement

The solution to the equation log3x4=log2x8\log_{3x} 4 = \log_{2x} 8, where xx is a positive real number other than 13\tfrac{1}{3} or 12\tfrac{1}{2}, can be written as pq\tfrac {p}{q} where pp and qq are relatively prime positive integers. What is p+qp + q?
<spanclass=latexbold>(A)</span>5<spanclass=latexbold>(B)</span>13<spanclass=latexbold>(C)</span>17<spanclass=latexbold>(D)</span>31<spanclass=latexbold>(E)</span>35<span class='latex-bold'>(A) </span> 5 \qquad <span class='latex-bold'>(B) </span> 13 \qquad <span class='latex-bold'>(C) </span> 17 \qquad <span class='latex-bold'>(D) </span> 31 \qquad <span class='latex-bold'>(E) </span> 35