Work Step by Step
The logarithmic function $\ln x$ is increasing, so for a greater input e.g. $b\gt a$, there is a greater output $\ln b\gt\ln a$. It is required that both $a$ and $b$ be greater than $0$ as logarithms can only be taken for positive values. So when $0\lt a\lt b, $ then $\ln a\lt\ln b$.