Natural Logarithm of 2 is Greater than One Half/Proof 2

Lemma

$\ln 2 \ge \dfrac 1 2$

where $\ln$ denotes the natural logarithm function.

Proof

\(\ds 1 - \frac 1 x\)

\(\le\)

\(\ds \ln x\)

Lower Bound of Natural Logarithm

\(\ds \leadsto \ \ \)

\(\ds \frac 1 2\)

\(\le\)

\(\ds \ln 2\)

letting $x = 2$

$\blacksquare$