How to solve $n\log_2(n) = C$?

Question

I am trying to solve the following equation:

$$ n\log_2(n) = C $$ with $C$ being a constant greater than $0$.

I thought about putting the $n$ that is outside the $\log$ on the power of the $n$ inside but that is surely not the way. I also thought about exponentiating everything but I can't see how that is going to help.

Can I please get some help? Thanks

Answer 1

Let $w = \log n$, $e^w = n$. Then $$we^w = C\log 2$$so that $w = W(C\log 2)$ where $W$ is the Lambert $W$ function, that is $n = \exp(W(C\log 2))$.