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December 12th, 2012, 05:34 PM  #1 
Newbie Joined: Dec 2012 Posts: 2 Thanks: 0  solution for a^x + bx  c =0
Please help me find a solution for x in following equation a^x + bx  c =0, where a, b, c are some arbitrary constant and x is a variable. If a=1.07, b = 3.774 x 10^3 and c = 1.5589, then x =6.5 satisfies the equation. However, I am finding it difficult to find a method for solving the equation other than from hit and trial. Thanks in advance. 
December 12th, 2012, 07:09 PM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: solution for a^x + bx  c =0 Quote:
You show: b = 3.774 x 10^3 ; what does that mean? is "x" a multiplication symbol? If so, start using * as multiplication symbol.  
December 12th, 2012, 07:14 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: solution for a^x + bx  c =0
× is also preferred over x, or · as well. (However, the asterisk is easiest to use since the others are not on the standard keyboard.)

December 13th, 2012, 09:49 PM  #4 
Newbie Joined: Dec 2012 Posts: 2 Thanks: 0  Re: solution for a^x + bx  c =0
Thanks for your help. Yes 'x' is not variable in b = 3.774 x 10^3. I should have used * sign instead. Thanks for your suggestion Denis, MarkFL. 
December 14th, 2012, 06:01 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 
Expressing x explicitly in terms of a, b and c requires a special function called the Lambert W function.

December 14th, 2012, 07:27 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: solution for a^x + bx  c =0
How is your 6.5 arrived at ? I make it ~19/3 (quite close to 6 1/3) 1.07^(19/3) + 3.774*10^(3)*(19/3)  1.5589 = .0000373... 

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