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Log of Divisors

Source: AMC 12 2008B Problem 23

February 28, 2008
logarithmsfloor functiongeometry3D geometrypyramidsymmetrynumber theory

Problem Statement

The sum of the base-10 10 logarithms of the divisors of 10n 10^n is 792 792. What is n n? <spanclass=′latex−bold′>(A)</span> 11<spanclass=′latex−bold′>(B)</span> 12<spanclass=′latex−bold′>(C)</span> 13<spanclass=′latex−bold′>(D)</span> 14<spanclass=′latex−bold′>(E)</span> 15 <span class='latex-bold'>(A)</span>\ 11\qquad <span class='latex-bold'>(B)</span>\ 12\qquad <span class='latex-bold'>(C)</span>\ 13\qquad <span class='latex-bold'>(D)</span>\ 14\qquad <span class='latex-bold'>(E)</span>\ 15
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