2014 AMC 10A Problems/Problem 25

The following problem is from both the 2014 AMC 12A #22 and 2014 AMC 10A #25, so both problems redirect to this page.

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The number $5^{867}$ is between $2^{2013}$ and $2^{2014}$ . How many pairs of integers $(m,n)$ are there such that $1\leq m\leq 2012$ and $5^n<2^m<2^{m+2}<5^{n+1}?$ $\textbf{(A) }278\qquad \textbf{(B) }279\qquad \textbf{(C) }280\qquad \textbf{(D) }281\qquad \textbf{(E) }282\qquad$

2014 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

2014 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2014 AMC 10A Problems/Problem 25

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