MathDB
Logarithm Equality

Source:

January 11, 2009
logarithms

Problem Statement

The number of real values of x x satisfying the equality (\log_2x)(\log_bx) \equal{} \log_ab, where a>0 a > 0, b>0 b > 0, a1 a \neq 1, b1 b \neq 1, is: <spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> a finite integer greater than 2<spanclass=latexbold>(E)</span> not finite <span class='latex-bold'>(A)</span>\ 0 \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ 2 \qquad <span class='latex-bold'>(D)</span>\ \text{a finite integer greater than 2} \qquad <span class='latex-bold'>(E)</span>\ \text{not finite}