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July 30th, 2010, 10:11 PM   #1
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Solutions to an equation

Hi,

How can i prove that the equation (ln|x|)^3 = x has three real solutions?

By using the Intermediate value theorem, i know that this equation has some solutions. I'm also trying to use Rolle's theorem but it's not getting me anywhere.

Thanks for any help
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July 31st, 2010, 02:00 AM   #2
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Re: Solutions to an equation

Are you sure?
ln|x| is symmetric, so is the cube of it. There are two real solutions, between -1 and 0, 6 and 7.
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July 31st, 2010, 04:31 AM   #3
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Re: Solutions to an equation

a third one as well, between 93 and 94.

Hoempa
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July 31st, 2010, 05:35 AM   #4
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Re: Solutions to an equation

Yes, there is a third one.
f(x)=ln≥|x|, use f'(x) with x>0.
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