2005 10A 13 · AMC 10 Step by Step

AMC 10 Step by Step

2005 AMC 10AProblem 13P11-15~3 minPrint

Exponents, Logarithms & Radicals Absolute Value & Inequalities Set up the equation/formula and compute; no special trick needed

How many positive integers $n$ satisfy the following condition:

$\left(130n\right)^{50} > n^{100} > 2^{200} \ \text{?}$

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.