MathDB
Logarithm equation

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November 21, 2005
logarithms

Problem Statement

There exist positive integers A,BA,B and CC, with no common factor greater than 11, such that Alog⁡2005+Blog⁡2002=C.A \log_{200} 5 + B \log_{200} 2 = C. What is A+B+CA+B+C?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> 10<span class='latex-bold'>(A)</span>\ 6 \qquad <span class='latex-bold'>(B)</span>\ 7\qquad <span class='latex-bold'>(C)</span>\ 8 \qquad <span class='latex-bold'>(D)</span>\ 9 \qquad <span class='latex-bold'>(E)</span>\ 10
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