Natural Logarithm (Base e)

The natural logarithm uses base $e \approx 2.718$ and is written as $\ln(x)$ or $\log_e(x)$. The number $e$ appears in continuous growth problems and calculus.

For example, $\ln(e) = 1$ and $\ln(e^2) = 2$. You'll see $\ln$ in probability, machine learning, and anywhere continuous growth models appear.

In Big-O analysis, the base doesn't matter because logarithms of different bases differ only by a constant factor. So $O(\log_2 n) = O(\ln n) = O(\log_{10} n)$. I'll explain why in a few units.