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Find the largest positive integer n such that n^{200} < 3^{500}.

 Jun 19, 2020
 #1
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This means

\(n^2 < 3^5\\ n^2 < 243\)

 

Because 152 = 225 < 243, and 162 = 256 > 243,

 

The largest n such that n200 < 3500 is n = 15.

 Jun 19, 2020
edited by MaxWong  Jun 19, 2020

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