Inequality with logarithms-please put the complete solution!

For students of class 9-10 (age 14-16)
simplythebest
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Joined:Thu Mar 01, 2018 3:19 pm
Inequality with logarithms-please put the complete solution!

Unread post by simplythebest » Thu Mar 01, 2018 3:28 pm

Let be $a,b,c,d>1$ with $abcd=16$. Prove that:
$log_{ab} (a+b)+log_{bc} (b+c) + log_{cd}(c+d)+log_{da}(d+a) \geq 4.$

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