Problem

Source: Turkmenistan National Math Olympiad 2012 Grade 9

Tags: inequalities, logarithms, inequalities proposed



Prove that : $\frac{1}{(\log_{bc} a)^n}+\frac{1}{(\log_{ac} b)^n}+\frac{1}{(\log_{bc} a)^n}\geq 3\cdot2^{n}$ where $a,b,c>1$ and $n$ is natural number.