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2018 AMC 12A Question 14

AMC12 · 2018 AMC 12A

Question 14

The solution to the equation $\log_{3x} 4 = \log_{2x} 8,$ where $x$ is a positive real number other than $\tfrac13$ or $\tfrac12,$ can be written as $\tfrac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. What is $p + q?$
  1. $5$
  2. $13$
  3. $17$
  4. $31$
  5. $35$