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Solution set of log equation

Source: 1959 AHSME Problem 23

August 14, 2013
logarithmsAMClogarithmalgebraAMC 12

Problem Statement

The set of solutions of the equation log⁡10(a2−15a)=2\log_{10}\left( a^2-15a\right)=2 consists of <spanclass=′latex−bold′>(A)</span> two integers <spanclass=′latex−bold′>(B)</span> one integer and one fraction <span class='latex-bold'>(A)</span>\ \text{two integers } \qquad<span class='latex-bold'>(B)</span>\ \text{one integer and one fraction}\qquad <spanclass=′latex−bold′>(C)</span> two irrational numbers <spanclass=′latex−bold′>(D)</span> two non-real numbers<spanclass=′latex−bold′>(E)</span> no numbers, that is, the empty set<span class='latex-bold'>(C)</span>\ \text{two irrational numbers }\qquad<span class='latex-bold'>(D)</span>\ \text{two non-real numbers} \qquad<span class='latex-bold'>(E)</span>\ \text{no numbers, that is, the empty set}
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