Natural Logarithm of 1 is 0/Proof 2

Theorem

$\ln 1 = 0$

Proof

We use the definition of the natural logarithm as the inverse of the exponential:

$\ln x = y \iff e^y = x$

Then:

\(\ds e^0\)

\(=\)

\(\ds 1\)

Exponential of Zero

\(\ds \leadstoandfrom \ \ \)

\(\ds \ln 1\)

\(=\)

\(\ds 0\)

$\blacksquare$