Logarithm Exponents
Source: AIME 2009II Problem 2
April 2, 2009
logarithmsAIMEalgebra
Problem Statement
Suppose that , , and are positive real numbers such that a^{\log_3 7} \equal{} 27, b^{\log_7 11} \equal{} 49, and c^{\log_{11} 25} \equal{} \sqrt {11}. Find
a^{(\log_3 7)^2} \plus{} b^{(\log_7 11)^2} \plus{} c^{(\log_{11} 25)^2}.