2015 Mock AIME I Problem 2: Logarithm System

Algebra Level 4

Suppose that xx and yy are real numbers such that logx3y=2013\log_x 3y = \frac{20}{13} and log3xy=23\log_{3x}y=\frac23. The value of log3x3y\log_{3x}3y can be expressed in the form ab\frac ab where aa and bb are positive relatively prime integers. Find a+ba+b.

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