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Home » Olympiad Section » Inequalities » Inequalities Unsolved Problems
 
An ineq related to logarithmic mean
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miwalin
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#1
An ineq related to logarithmic mean
Let a,b>0 and x\in [0,\frac{1}{2}]. Prove or disprove (a-b)^2\le 2(a^xb^{1-x})^2(lna-lnb)^2.

PostPosted: Sun Nov 08, 2009 3:03 pm  Back to top 
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panyi2009
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#2
The inequality does not hold when x=0. Simply choose x=0, a=2b, LHS = b^{2}, RHS =2b^{2}(ln2)^{2} < b^{2}

PostPosted: Sun Nov 08, 2009 7:09 pm  Back to top 
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