solve x=-ln(x)

[Chazef]

calculator says that x=0.567143.... and that more solutions may exist. I don't think this is in the course (at least not in the chapter I'm doing) but does anybody know the process for solving something like this?

[pi]

Not unless you're familiar with uni concepts such as http://mathworld.wolfram.com/LambertW-Function.html

[brightsky]

consider the function f(x) = x+ln(x). then compute the numerical approximation using newton's method [you make an initial guess, then find the x-intercept of the tangent line at that point and repeat a gazillion times until you are satisfied with the approximation]. very boring stuff.

you won't be asked to solve transcendental equations in methods.

[Chazef]

reading stuff like that really makes me appreciate the awesomeness of math, even though I understood almost none of it
EDIT: was referring to that wolfram page