how to solve the logarithmic equation which has both n and logn How to solve this logarithmic equation? $8n^2 = 64n\log n$, ($\log n$ here is base 2)
I have tried to convert it to $n-8\log n = 0$, but how to solve the latest?

This doesn't have any solutions using elementary functions. But, using the Lambert W function, we get: $$n = -\frac {8}{\ln 2} \operatorname{W} \left (-\frac {\ln 2}{8} \right)$$ and $$n = -\frac {8}{\ln 2} \operatorname{W}_{-1} \left (-\frac {\ln 2}{8} \right)$$
