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January 28th, 2012, 12:58 AM   #1
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Hard logarithm question

Hello!

Attached is a very hard logarithm question that I couldn't answer in my math test. If someone could help me answer it, I would very much appreciate it

Thanks in advance
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January 28th, 2012, 01:13 AM   #2
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Re: Hard logarithm question

You are given:

Your first step to make a common denominator for the RHS is a good start:

Now use some logarithm rules:





To continue make the substitution which will give you a quadratic equation in
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January 28th, 2012, 01:20 AM   #3
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Re: Hard logarithm question

We are given to solve:





Multiply through by as we know for all real x:



Arrange as quadratic on :



Factor:



Assuming x is real, we must discard the negative root, and are left with:



Convert from exponential to logarithmic form:

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January 28th, 2012, 02:23 AM   #4
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Re: Hard logarithm question

Thank you!

I'm really impressed with this forum, the answers are clear and succinct
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January 22nd, 2017, 01:45 AM   #5
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Answer

x = log[base 5](3) - 1

Last edited by Wizzy0630; January 22nd, 2017 at 01:47 AM.
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May 31st, 2017, 02:37 AM   #6
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Answer

Hey,

I know I may be too late to answer you now.

You do not need to use logarithm for this question. Set 5^x as y, and rewrite the equation as 2*5*y = 1+3/y. Then continue the equation and factorize the quadratic you get. Keep going until you get your answer.

Thanks
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