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How to solve for the equation $ax \exp(bx)=c$? It is known that $x\geq 0$.

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Solving this equation requires the Lambert W-function, which when applied to c gives the solution for a=b=1. Barring trivial cases, I don't think there's any easier way to derive it.

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    In general, we can rewrite the equation as $(bx) \exp(bx) = \frac{bc}{a} = d$ (say). The solution for this is $bx = W(d)$, or $x = \frac{1}{b}W(d)$.2011-11-23
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    Srivatsan's comment ought to be the answer, methinks.2011-11-24
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    Thanks, it is helpful. And what about more general equation ax*exp(bx+p)=c? And how to find a solution for W(d), if d>=0 and is supposed to be a real number?2011-11-25
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    ax*exp(bx)*exp(p)=c, then bx*exp(bx)=b*(c/a)*exp(-p)=d. Am I right? Let d = 5. How to find the value of W(d)? Taylor series expansion around 0?2011-11-25
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    @Sergei: Why not ask a new question?2011-12-04