# Easy Peasy..!!

Algebra Level 3

$\large \log_{\sqrt[2]{3}} (x+y) = 2 , \log_{\sqrt[3]{5}} (x-y) = -3$

The system of equation above holds true for real numbers $$x$$ and $$y$$. If $$2x+5y$$ can be written as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a-b$$.

×