Simple problem: The equation below has two solutions for $x$ for a range of parameter values (see below). This is straightforward to see graphically. I need to find both of these solutions. Some additional information:
- Approximations are OK if necessary
- Ideally both solutions will be found, but ideas for finding either individually are also helpful
- In the equation below: $k \approx 0.1$, $n \approx 2.5$
The equation:
$\frac{1}{n} e^{-n(1-e^{-x/n})}e^{\frac{x}{n}} = 1-e^{ (x/n^2)(1-e^{-x/n})^{-1}e^{\frac{x}{n}}k}$