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 \(a+b\).
by
David Altizio