Logarithm of 1 is 0

Theorem

$\ln 1 = 0$

where $\ln 1$ denotes the natural logarithm of $1$.

Proof 1

From the definition of natural logarithm:

$\displaystyle \ln x = \int_1^x \frac {dt} t$

From Integral on Zero Interval:

$\displaystyle \ln 1 = \int_1^1 \frac {dt} t = 0$

$\blacksquare$