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a and b

Source:

October 16, 2005
logarithms

Problem Statement

If a a and b b are positive numbers such that a^b \equal{} b^a and b \equal{} 9a, then the value of a a is: <spanclass=′latex−bold′>(A)</span> 9<spanclass=′latex−bold′>(B)</span> 19<spanclass=′latex−bold′>(C)</span> 99<spanclass=′latex−bold′>(D)</span> 93<spanclass=′latex−bold′>(E)</span> 34 <span class='latex-bold'>(A)</span>\ 9\qquad <span class='latex-bold'>(B)</span>\ \frac {1}{9}\qquad <span class='latex-bold'>(C)</span>\ \sqrt [9] {9}\qquad <span class='latex-bold'>(D)</span>\ \sqrt [3] {9}\qquad <span class='latex-bold'>(E)</span>\ \sqrt [4] {3}
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