Main Question or Discussion Point
I understand the rational for using the Lambert W. function for solving equations such as [tex]x^x = z [/tex], where no derivative in terms of elementary functions exists for the expression. However, on the Wikipedia page about the Lambert W. function, an example is given with the equation [tex]2^t = 5t[/tex]. In this case (since numerical evaluation of the W. function boils down to Newton's method in the end) is there any advantage to using the W. function instead of Newton's method directly to solve the equation, other than just getting it in an explicit formula for t? Thanks!