The largest integer n for which n^200<5^300 is

1984 AMC 12 Problem 5

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The largest integer

n

for which

n^{200}\lt5^{300}

8

9

10

11

12

Take the positive one-hundredth root of both sides

Compare

n^2

with

5^3

Taking positive one-hundredth roots gives

n^2\lt5^3=125.

Since

11^2=121\lt125

but

12^2=144\gt125,

the largest possible integer is

11.

Therefore, the correct answer is D.