# problems with Euler's number..

• July 17th 2011, 12:54 PM
JamesBond16
problems with Euler's number..
1-e^(-x)=5e^(-2x)+3x^(-x)
• July 17th 2011, 12:58 PM
e^(i*pi)
Re: problems with Euler's number..
I don't think there is an analytical way to solve because of the $x^{-x}$ term. Should that read $e^{-x}$ per chance?
• July 17th 2011, 01:03 PM
JamesBond16
Re: problems with Euler's number..
3x^(-x) is correct
• July 17th 2011, 02:57 PM
Also sprach Zarathustra
Re: problems with Euler's number..
If $f(x)=1-e^{-x}-5e^{-2x}-3x^{-x}$

Then, $f(1)<0$ and $f(3)>0$, so there is at least one root in $[1,3]$.