# Thread: problems with Euler's number..

1. ## problems with Euler's number..

1-e^(-x)=5e^(-2x)+3x^(-x)

2. ## 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?

3. ## Re: problems with Euler's number..

3x^(-x) is correct

4. ## 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 $[1,3]$.