Logarithm equation

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
JC531
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Logarithm equation

Postby JC531 » Mon Mar 17, 2014 1:13 am

Hello PM! My teacher assigned my group in class a set of logarithm problems to solve. Yet I'm finding mine to be super tough.

The problem is:

ln(x2)=log5(x-1)

I have no idea how to solve it. I've tried several different methods of condensing and expanding the problem but I still can't get it to where I can solve it.

One way I've gotten is 2logeX=log5(X-1) but still I get lost there. I think its the (X-1) that keeping me from knowing what to do.

Please Help!

Thanks :)

Alfred
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Re: Logarithm equation

Postby Alfred » Mon Mar 17, 2014 5:27 am

JC531 wrote:log5(x-1)

Did you know that equals log(x-1) / log(5) ?

buddy
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Re: Logarithm equation

Postby buddy » Mon Mar 17, 2014 11:59 am

JC531 wrote:ln(x2)=log5(x-1)

I have no idea how to solve it.

Do change of base to make the logs the same base. So ln(x^2) = log_5(x^2)/log_5(e) = 2log_5(x)/log_5(e) or log_5(x-1) = ln(x-1)/ln(5). Then solve.

JC531
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Re: Logarithm equation

Postby JC531 » Mon Mar 17, 2014 12:31 pm

Could you go through steps on how you got to those and how to solve them? I wrote down what you put but I don't understand how you got to each equation. Thanks again for the help!

buddy
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Re: Logarithm equation

Postby buddy » Mon Mar 17, 2014 10:15 pm

JC531 wrote:Could you go through steps on how you got to those and how to solve them? I wrote down what you put but I don't understand how you got to each equation.

There's no steps. You just plug into the formula at the link. Like log_3(10) = ln(10)/ln(3) for example. What are you getting when you plug into it?

JC531
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Re: Logarithm equation

Postby JC531 » Tue Mar 18, 2014 1:16 am

Well. Just found out by my teacher today that there is no solution. After going as far as we did if you were to graph each side of the equation the graphs never meet.


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