Is it possible to solve for $x$ which satisfies the equation $$d=(a\exp(bx)+\exp(cx))x^2$$ where $a,b,c,d$ are given constants? It looks quite horrible... Many thanks!
Is an equation of the following form solvable?
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exponentiation
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0Looks doubtful; you have the sum of two independent exponentials in there, which precludes the use of things like the Lambert function... – 2012-08-24
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0Yes, it **is** quite horrible. It is not possible in terms of elementary functions. Numerical procedures are always available. And, at least for limited ranges for the parameters, there may be good approximate *formulas*. – 2012-08-24