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March 29th, 2014, 07:40 PM   #1
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Problem with ln

Hi, Can anyone solve this algebraically? I found the answer to be 15.36 using wolfram, but I can't figure out how to do it myself. Thanks!

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March 29th, 2014, 08:07 PM   #2
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Google "solving numerically".
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March 30th, 2014, 12:33 PM   #3
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Divide through by 10000. It looks simpler.
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March 30th, 2014, 06:50 PM   #4
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The equation is equivalent to (x/20 - 1)e^(x/20 - 1) = -1/(2e),
which can be solved by use of the Lambert W function.

One gets x = -33.567 or 15.361 (both rounded to 3 decimal places).
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