Someone who can explain ??

[rurin]

Our teacher told us to solve this: e^x = -x

We are not even close to this topic yet and he also said it was just a joke, but now I'm really curious how to solve this.

Would someone be so nice to explain it to me?

 

I know it is difficult, because not even my teacher has solved it yet... but I find this so fascinating that someone can actually find an answer xD

[ajb]

You need the Lambert W-function, which gives you solutions to

 

[math]f[w] = w e^{w}[/math].

 

The principle solution is also known as the product log.

 

The principal answer to your question is

 

[math]x = - ProductLog[1] \cong -0.567143[/math]

 

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The number Productlog[1] is also called the Omega constant.

Edited January 29, 2013 by ajb