I am trying to iterate $\frac{x-1}{x\ln{x}} - a= 0$ to solve for $x$ using Newton Raphson, but it is blowing up. Any ideas why? Is this a strange function to find a root for?
$$x_{i+1} = x_i - f(x_i)/f'(x_i)$$ where $$f'(x) = \frac{-x+\ln(x)+1}{x^2 \ln(x)}$$