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Juan Set 1 Paper 1 · Q12

Paper 1Powers & logarithms

Let aa and bb be non-consecutive positive integers such that

ln⁡(a!)=ln⁡(b!)+3ln⁡2+2ln⁡3+ln⁡7.\ln(a!)=\ln(b!)+3\ln2+2\ln3+\ln7.

What is a+ba+b?

(Note that n!=n⋅(n−1)⋅(n−2)⋯3⋅2⋅1n!=n\cdot(n-1)\cdot(n-2)\cdots3\cdot2\cdot1)

A10
B13
C15
D18
E20

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