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#1 2012-09-11 19:29:24

n1corponic
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Natural logarithms problem (ln)

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 (2012-09-11 19:36:19)

#2 2012-09-11 19:50:36

bobbym
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Re: Natural logarithms problem (ln)

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2012-09-11 20:01:21

n1corponic
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Re: Natural logarithms problem (ln)

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.

#4 2012-09-11 20:05:08

bobbym
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Re: Natural logarithms problem (ln)

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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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