I need to prove that the following inequality is true only if t=0, t=1 or a=b>0:

I have no idea how to proceed.

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- Nov 29th 2009, 07:24 PMdannyboycurtisHolder's Inequality
I need to prove that the following inequality is true only if t=0, t=1 or a=b>0:

I have no idea how to proceed. - Nov 30th 2009, 04:12 AMEnrique2
The inequality is true for each 1<t<1 also! it is just the main ingredient for proving Holder inequality. Since log is incresing, the inequality is equivalent to

Now apply basic properties of the logarithm to the left hand side and use that log is concave to conclude. - Nov 30th 2009, 04:17 PMdannyboycurtis
Im not sure how to apply the concept of concavity to this problem...

- Nov 30th 2009, 11:39 PMredsoxfan325