Is there a simple analytic method to solve for n in this equation?

Question

$n\cdot2^n = r,\; r \in \mathbb{Q}, n \in \mathbb{R}$

I'm trying to solve for the input size of a $n\cdot \log_2 n$ algorithm, i.e. I started out with $n\cdot \log_2 n = 100$

Answer 1

$$n = \dfrac{W(r \ln(2))}{\ln(2)}$$ where $W$ is the Lambert W function