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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,917

I have been stuck with this enigma for minutes now..

12. Suppose A and B are positive real numbers such that logA(B)=logB(A). Algebraically prove the value of AB. A does not equal B, and neither A nor B = 1.

My thoughts: change of base formula could be useful, but I have been utilizing it for minutes now and it always seems to coverge to log(a)=log(b) which is useless.

*Last edited by Mathegocart (2017-03-30 14:39:51)*

The integral of hope is reality.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Algebraically prove the value of AB.

Can you explain that?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Mathegocart****Member**- Registered: 2012-04-29
- Posts: 1,917

Your method should compose of a list of steps such that the last one ends in AB = (number)

The integral of hope is reality.

May bobbym have a wonderful time in the pearly gates of heaven.

He will be sorely missed.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

All the solutions I am getting are of the form A = c, B = 1 / c for some real c, which means AB=1. See if you can algebraically fight your way to that conclusion.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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