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

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SUMMARY

The discussion centers on comparing the values of 2^500 and 5^200. A participant transformed 2^500 into 4^250 for easier comparison, suggesting that 4^250 appears larger than 5^200. The solution involves manipulating the expressions to find a common base, ultimately leading to the conclusion that 2^500 is greater than 5^200 through algebraic proof.

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Icelove
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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.
 
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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
 

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