MathDB
Maximizing a Log

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April 6, 2013
logarithms

Problem Statement

Let aa and bb be real numbers greater than 11 for which there exists a positive real number cc, different from 11, such that 2(log⁡ac+log⁡bc)=9log⁡abc.2(\log_ac+\log_bc)=9\log_{ab}c. Find the largest possible value of log⁡ab\log_ab.
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>6<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A) </span>\sqrt2\qquad<span class='latex-bold'>(B) </span>\sqrt3\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>\sqrt6\qquad<span class='latex-bold'>(E) </span>3
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