Natural Logarithm of 1 is 0/Proof 1

Theorem

$\ln 1 = 0$

Proof

We use the definition of the natural logarithm as an integral:

$\ds \ln x = \int_1^x \frac {\d t} t$

From Integral on Zero Interval:

$\ds \ln 1 = \int_1^1 \frac {\d t} t = 0$

$\blacksquare$