2015 Mock AIME I Problem 2: Logarithm System

Algebra Level 4

Suppose that \(x\) and \(y\) are real numbers such that \(\log_x 3y = \frac{20}{13}\) and \(\log_{3x}y=\frac23\). The value of \(\log_{3x}3y\) can be expressed in the form \(\frac ab\) where \(a\) and \(b\) are positive relatively prime integers. Find \(a+b\).

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