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#1 2017-03-30 14:35:53
- Mathegocart
- Member
- Registered: 2012-04-29
- Posts: 2,226
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.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.
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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: 2,226
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.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.
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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.
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