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Registered Member #1617
Joined: Fri Aug 01 2008, 07:31AM
Location: Adelaide, South Australia
Posts: 139
hi all,
does anyone know if there is an analytical way to find a solution to an equation of the form bx+Ce^(x)=0, rather than using a numerical method like newtons rule?
Registered Member #58
Joined: Thu Feb 09 2006, 05:40AM
Location: Tri-Cities, Washington, US
Posts: 317
hmm i wasn't able to solve it normally. I got: Ce^(x)=-bx ln(Ce^(x))=ln(-bx) ln(c)+ln(e^x)
=ln(-b)+ln(x) ln(c)+x=ln(-b)+ln(x) x-ln(x)=ln(-b)-
ln(c) x-ln(x)=ln(-b/c) take e^ of both sides
-c/b = x/e^x = xe^-x, so c/b = (-x)e^(-x), so -x = W(c/b), x = -W(c/b)
where W is the lambert fuction where W is the inverse of f(z)=ze^z
Registered Member #1617
Joined: Fri Aug 01 2008, 07:31AM
Location: Adelaide, South Australia
Posts: 139
Thanks Mike, i didn't know about the lambert function. I see on the wikipedia article "the lambert function cannot be expressed in terms of elementry function", I'm not all that good with maths, but does this mean that the only way to evaluate it in general is by its tayor series or some other numerical method? this is what i originally meant with my question (i should have been a bit clearer). Thanks for the help.
edit: I see now on the wikiarticle about numerical evaluation. Thanks
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a mathematical question
