Question: Prove that the function $f(x)=\log _{e} x$ is increasing on $(0, \infty)$.
Solution:
let $x_{1}, x_{2} \in(0, \infty)$
We have, $x_{1}
$\Rightarrow \log _{e} x_{1}<\log _{e} x_{2}$
$\Rightarrow f\left(x_{1}\right)
So, $f(x)$ is increasing in $(0, \infty)$
