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#1 2017-03-30 14:35:53

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Logarithmic Problem

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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#2 2017-03-30 14:51:53

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

Re: Logarithmic Problem

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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#3 2017-03-30 14:56:03

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,882

Re: Logarithmic Problem

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


The integral of hope is reality.

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#4 2017-03-30 15:22:39

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

Re: Logarithmic Problem

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.

Offline

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