As easy as it looks

Algebra Level 3

Find the largest integer n n for which n 200 < 5 300 n^{200} < 5^{300} .

12 9 11 10

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1 solution

Kay Xspre
Feb 29, 2016

Take the 100th root. This will give n 2 < 5 3 n 2 < 125 n^2 < 5^3\Rightarrow n^2 < 125 Hence the maximum n n is n = 11 n = 11

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