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2014 AMC 10A Problem 25

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2014 AMC 10A Problem 25AMC 10 Step by Step
Name:                             Date: September 13, 2026
Exponents, Logarithms & Radicals · difficulty 5 of 5 · about 8 min · position P21-25

The number 58675^{867} is between 220132^{2013} and 220142^{2014} . How many pairs of integers (m,n)(m,n) are there such that 1≤m≤20121\leq m\leq 2012 and 5n<2m<2m+2<5n+1?5^n<2^m<2^{m+2}<5^{n+1}?

  1. A)

    278278

  2. B)

    279279

  3. C)

    280280

  4. D)

    281281

  5. E)

    282282

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