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- Feb 14, 2012

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Hi all, I've been having a hard time trying to solve the following inequality:

Prove that $\displaystyle \left(\log_{24}(48) \right)^2+\displaystyle \left(\log_{12}(54) \right)^2 >4$

I've tried to change the bases to base-10 log and relating all the figures (12, 24, 48, and 54) in terms of 2 and 3 but only to make the problem to be more confounded.

Could I get some hints on how to tackle this problem?

Any help would be deeply appreciated.

Thanks!

P.S. This question was originally asked here (Logarithm) at MMF.

Prove that $\displaystyle \left(\log_{24}(48) \right)^2+\displaystyle \left(\log_{12}(54) \right)^2 >4$

I've tried to change the bases to base-10 log and relating all the figures (12, 24, 48, and 54) in terms of 2 and 3 but only to make the problem to be more confounded.

Could I get some hints on how to tackle this problem?

Any help would be deeply appreciated.

Thanks!

P.S. This question was originally asked here (Logarithm) at MMF.

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