Math Problem Statement
Find the minimum value of : \frac{{{{\log }a}\left( {bc} \right) + {{\log }b}\left( {ac} \right) + {{\log }c}\left( {ab} \right)}}{{{{\log }{ab}}c + {{\log }{bc}}a + {{\log }{ca}}b}} where a, b, c ∈ (0, 1) ∪ (1, ∞).
Solution
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Math Problem Analysis
Mathematical Concepts
Logarithms
AM-GM Inequality
Formulas
Logarithmic identities
AM-GM inequality
Theorems
Arithmetic Mean-Geometric Mean Inequality (AM-GM Inequality)
Suitable Grade Level
Advanced High School / College
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