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Algebraic Equation

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March 3, 2010
logarithms

Problem Statement

The set of x x-values satisfying the equation x^{\log_{10} x} \equal{} \frac{x^3}{100} consists of: <spanclass=′latex−bold′>(A)</span> 110<spanclass=′latex−bold′>(B)</span> 10, only<spanclass=′latex−bold′>(C)</span> 100, only<spanclass=′latex−bold′>(D)</span> 10 or 100, only<spanclass=′latex−bold′>(E)</span> more than two real numbers. <span class='latex-bold'>(A)</span>\ \frac{1}{10} \qquad <span class='latex-bold'>(B)</span>\ \text{10, only} \qquad <span class='latex-bold'>(C)</span>\ \text{100, only} \qquad <span class='latex-bold'>(D)</span>\ \text{10 or 100, only} \qquad <span class='latex-bold'>(E)</span>\ \text{more than two real numbers.}
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