Prove that the function
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, $x_{1}<x_{2}$

$\Rightarrow \log _{e} x_{1}<\log _{e} x_{2}$

$\Rightarrow f\left(x_{1}\right)<f\left(x_{2}\right)$

So, $f(x)$ is increasing in $(0, \infty)$