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**n1corponic****Member**- Registered: 2012-09-10
- Posts: 7

Hello all! I am new here and I am a student having a hard time in math. I have the following natural logarithms problem and it is giving a hard time. Can someone please help with the solution? And also if possible evaluate the difficulty of this problem?

Solve for x: 4^x-4^(x-1)=3^(x+1)-3^x

*Last edited by n1corponic (2012-09-10 21:36:19)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi n1corponic;

I might be missing something but I would say very difficult. I do not see a way using algebra so you have to use the methods of numerical analysis. This will require a computer or a programmable calculator.

A little background:

1) Where does the problem come from? This will determine what methods can be used.

2) Are you just interested in a solution?

3) What type of solution, real or complex?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**n1corponic****Member**- Registered: 2012-09-10
- Posts: 7

Hi Bobbym! I don't think i have to find a rational number. Usually the answer to these logarithmic problems is smth like x=ln3/ln5 .To answer your great questions:

1)It comes from the book called Essential Mathematics for Economic Analysis 4th edition on page 123 problem 3.(a)

2)I am mostly interested in the logical thinking **process **in these kind of problems.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,347

Hi;

There is a simple answer according to Mathematica.

Seems like I spoke to soon. You can derive it like this:

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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