My Math Forum Problem with ln

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 March 29th, 2014, 07:40 PM #1 Senior Member   Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0 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! 0=-100000exp[-x/20]-10000x+200,000
 March 29th, 2014, 08:07 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Google "solving numerically".
 March 30th, 2014, 12:33 PM #3 Global Moderator   Joined: May 2007 Posts: 6,835 Thanks: 733 Divide through by 10000. It looks simpler.
 March 30th, 2014, 06:50 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,036 Thanks: 2274 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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