Which is larger: 2^500 or 5^200?

[Icelove]

Homework Statement

Which is bigger 2^500 or 5^200

Homework Equations

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The Attempt at a Solution

Well I got to 2^2^250 -> 4^250 vs 5^200... by the looking at it 4^250 is bigger but I can't just say it looks bigger... There are lots of these that I can't get on a common base, so if anyone can point me to the right direction I'll give lots of love.

 

[magwas]

divide the two numbers.
come to a form of (a/b^n)^k * a^k = (a*(a/b^n))^k
prove that a/b^n > 1/a
from that you can easily proove that the numerator is bigger than the denominator