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February 2nd, 2011, 07:48 AM   #1
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Help solving a problem

Hi all, first post and I didn't know exactly where to put this.

Does anybody know how to solve for x an equation of the form:

10 + ln(x) = 5x

Thanks
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February 2nd, 2011, 10:25 AM   #2
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Re: Help solving a problem

You have to use "numerical methods" to get approximate solutions.
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February 2nd, 2011, 11:47 AM   #3
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Re: Help solving a problem

If possible, rearrange so that the left-hand side is of the form and the right-hand side is a constant, then take the Lambert W of both sides.



The Lambert W is double-valued over the interval [-1/e, 0). This gives you two solutions, 0.00004541 and 2.15341058.
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February 2nd, 2011, 06:12 PM   #4
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Re: Help solving a problem

Thanks for the help! Never heard of the Lambert W before.
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February 2nd, 2011, 06:14 PM   #5
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Re: Help solving a problem

Quote:
Originally Posted by kevinp123
Thanks for the help! Never heard of the Lambert W before.
Me neither, obviously!
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