How to prove ln(n) = Θ(log2 n)?
You correctly pointed out that $\ln n = \frac{\log_2n}{\log_2 e}$. You can rewrite this as $\ln n = \frac{1}{\log_2e}\cdot\log_2n$. Since $\Theta(\cdot) $ allows you to drop constant factors (and as @Pseudonym pointed out, $\frac{1}{\log_2e}$ is constant), it follows that $\ln n = \Theta(\log_2n)$