I intend to solve the following problem n*log(n)=c, where log is base 10. n*log(n)=c, expressing this as n=10^(c/n), then this becomes n^n=10^c. Now this can be solved using a numerical method such as Lambert W function. The Lambert W function solves the problem x*e^(x)=c, where c is a constant, we can use this to solve our problem. ln(x)*e^(ln(x))= ln(c). Lets say I want find n*log(n)=100, then using this method I find n=56.9612. Which is correct, but what happens as c approaches a very large value such as 10*10^9? Is there no solution for this? This is an assignment but I am getting infinity as a solution since c is too large, any ideas?