Exponential of Natural Logarithm

Theorem

Let $x \in \R$ be a real number.

Let $\exp x$ be the exponential of $x$.

Then:

$\forall x > 0: \exp \left({\ln x}\right) = x$

$\forall x \in \R: \ln \left({\exp x}\right) = x$

Proof

This follow directly from the fact that the exponential function is the inverse of the natural logarithm function.

$\blacksquare$