Logarithm Tends to Infinity/Proof 2

Theorem

$\ln x \to +\infty$ as $x \to +\infty$

Proof

From the definition of the natural logarithm:

\(\ds \ln x\)

\(=\)

\(\ds \int_1^x \dfrac 1 t \rd t\)

The result follows from Integral of Reciprocal is Divergent.

$\blacksquare$

Sources

• 2005: Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus (8th ed.): Appendix $A$: Properties of the Natural Logarithmic Function