Graph of the Natural Logarithm $y = \ln x$

$y = \ln x$ is the inverse of $e^x$: it gives the power to which $e$ must be raised to obtain $x$. Its domain is $x > 0$ and its range is all real numbers.

It passes through $0$ at $x = 1$ and diverges to $-\infty$ as $x \to 0^+$ (the $y$-axis is an asymptote). It satisfies $\ln(ab) = \ln a + \ln b$, turning multiplication into addition.