# Fastest way to check if xy>yxx^y > y^x?

What is the fastest way to check if $x^y > y^x$ if I were writing a computer program to do that?

The issue is that $x$ and $y$ can be very large.

If both $x$ and $y$ are positive then you can just check:
so if both $x$ and $y$ are greater than $e \approx 2.7183$ then you can just check: