Question

Prove that the logarithmic function is strictly increasing on $(0, ∞)$.

Answer 1

The given function is f(x) = log x.

∴f'(x) = $\frac 1x$

It is clear that for x>0, f'(x) = $\frac 1x$ >0.

Hence, f(x) = log x is strictly increasing in interval (0, ∞).