# 2015 Mock AIME I Problem 2: Logarithm System

Algebra Level 5

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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