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I'm struggling with solving $x$ for the following equation: it looks in the form as $$e^x x^n=1-cx$$ where $c$ is just some constant number.

I tried to solve $x$ explicitly. But it seems not be able to do so. Do I have to solve it analytically using some Newton-Raphson method?

Many thanks!

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    Do you need to solve it over reals, or complexes? Is $n\in \mathbb{N}$? Is $c$ positive? negative? real?2012-08-31
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    $0, 1, 2, 3$ [solution depending](http://www.wolframalpha.com/input/?i=+Plot+e^%28x+%2B+n+ln%28x%29%29%2C+where+n%3D-2%2C+-1%2C+0%2C+1%2C+2) on the values of $n$ and $c$2012-08-31
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    Newton-Raphson method is a numerical method and you have to specify a value for c.2012-08-31

2 Answers 2