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March 25th, 2014, 12:11 PM  #1 
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Solve multiple term exponential
If I take the log of both sides, I get rid of the e on the right, but then I'm stuck with an ln on the left. How do I solve this? What I tried? Seems no better off than the start. P.S. Calculator not allowed 
March 25th, 2014, 12:34 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,834 Thanks: 733  Re: Solve multiple term exponential
There is no exact solution.

March 25th, 2014, 12:37 PM  #3 
Senior Member Joined: Sep 2009 Posts: 251 Thanks: 0  Re: Solve multiple term exponential
Really? There must be an exact solution.

March 26th, 2014, 07:11 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,019 Thanks: 2252 
The equation is equivalent to 18e^1.2 = (0.006x + 1.2)e^(0.006x + 1.2), so x = W(18e^1.2)/0.006  200, where W denotes the Lambert W function. 

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