# How do you simplify  ln 0?

$\ln 0$ is undefined, always.
If $a = \ln 0$ then ${e}^{a} = 0$, but ${e}^{z} \ne 0$ for all numbers $z$, whether Real or Complex.
In fact, the range of ${e}^{z} : \mathbb{C} \to \mathbb{C}$ is $\mathbb{C} \text{\} \left\{0\right\}$, so $0$ is the only number which does not have a logarithm.