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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). 