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Logarithmic Equations

Source: 2010 AIMEII Problem 5

April 1, 2010
logarithmsSFFTspecial factorizationsAMC

Problem Statement

Positive numbers x x, y y, and z z satisfy xyz \equal{} 10^{81} and (\log_{10}x)(\log_{10} yz) \plus{} (\log_{10}y) (\log_{10}z) \equal{} 468. Find \sqrt {(\log_{10}x)^2 \plus{} (\log_{10}y)^2 \plus{} (\log_{10}z)^2}.
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