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 $n\cdot \log_2 n = 100$

Look up the Lambert W function. Heads up, the solution to $x log x = 100$ is almost certainly not an integer. — Vik78, Oct 23 '16 at 20:26

score 1 · Accepted Answer · answered Oct 23 '16 at 20:25

1

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

answered Oct 23 '16 at 20:25

Robert Israel

1 Answers1