Prove that the function `f(x)=(log)_e x` is increasing on `(0,oo)dot`

Explanation

Let `x_1, x_2 in(0, infty)` such that `x_1 < x_2`. Then,

`x_1 < x_2`

`Rightarrow log _e x_1 < log _e x_2`

`Rightarrow f(x_1) < f(x_2)`

`therefore x_1 < x_2 Rightarrow f(x_1) < f(x_2), forall x_1, x_2 in(0, infty)`

So, `f(x)` is increasing on `(0, infty)`.