Finding the fixed point of a 1 dimensional map.

Question

I am struggling with finding the fixed point x* as a function of r for the one dimensional map: $$x_{n+1}=f(x)=x_n+log(r(2-x_n))$$ The solution is apparently: $$x_n^*=2-1/r$$ I understand a fixed point as fulfilling $$f(x_n^*) = x^*_n$$ but I am really struggling with figuring out how you're suppose to analytically find it for equations such as the one above.