The logarithm function [tex]\log_ab[/tex], where [tex]a,b>0 \wedge a\not =1[/tex], is increasing for [tex]a\in(1,\infty)[/tex] and decreasing for [tex]a\in(0,1)[/tex]
[tex]\ln x =\log_ex[/tex] and [tex]e\approx 2.7>1[/tex] therefore [tex]\ln x[/tex] is increasing.
