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Greatest Power of 2 that Divides Exponent

Source: 2014 AMC 12B #15

February 20, 2014

logarithmsblogsAMC

Problem Statement

When

p = \sum_{k=1}^{6} k \ln{k}

, the number

e^p

is an integer. What is the largest power of

2

that is a factor of

e^p

?

{<span class='latex-bold'>(A)</span>\ 2^{12}\qquad<span class='latex-bold'>(B)</span>\ 2^{14}\qquad<span class='latex-bold'>(C)</span>\ 2^{16}\qquad<span class='latex-bold'>(D)</span>}\ 2^{18}\qquad<span class='latex-bold'>(E)</span>\ 2^{20}

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