My Math Forum solution for a^x + bx - c =0

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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
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Re: solution for a^x + bx - c =0

Quote:
 Originally Posted by niraj 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.
a^x + bx - c = 0 : cannot be solved directly; numeric method required (or hit and miss!)...

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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