So I came across this equation:

xe^x=1

how would you solve that? there seems to be no analytical way of solving it. my teacher said something about iteration but any help would be appreciated. thanks!

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- Nov 13th 2010, 10:45 AMYehiaSolving xe^x = 1
So I came across this equation:

xe^x=1

how would you solve that? there seems to be no analytical way of solving it. my teacher said something about iteration but any help would be appreciated. thanks! - Nov 13th 2010, 10:50 AMrtblue
Well, from intuition, we see that x=0 is a viable option.

multiply both sides by xe.

add the exponents on the left side, and we get:

- Nov 13th 2010, 10:57 AMYehia
- Nov 13th 2010, 11:11 AMFernandoRevilla
- Nov 13th 2010, 12:54 PMEducated
I agree that x = 0 cannot be a solution.

Use the Lambert W function or an approximation method, like the Newton Raphson Method, to solve for x.

The Lambert W function has a simple solution, or if you plan to use the Newton Raphson method: then - Nov 14th 2010, 07:58 AMrtblue
Look at the given function. If x = 0, then the whole left side becomes one. Anything to power zero is one.

- Nov 14th 2010, 08:26 AMUnknown008
Yes, but if x becomes 0, you have

- Nov 14th 2010, 09:09 AMWilmer
x = ~.56714....

- Nov 14th 2010, 11:18 AMskeeter
Newton's method - Wikipedia, the free encyclopedia

,

since f(x) is continuous, there exists a zero between x = 0 and x = 1

Newton's method ...

let

continued iterations will be extremely close to