Mark the correct alternative in the following:

Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on $(a, b)$ is that $f^{\prime}(x)>0$ for all $x \in(a, b)$

$f(x)=\log _{a} x$

$\frac{\mathrm{d}(\mathrm{f}(\mathrm{x}))}{\mathrm{dx}}=\frac{1}{\mathrm{x} \log _{\mathrm{e}} \mathrm{a}}=\mathrm{f}^{\prime}(\mathrm{x})$

For increasing $f^{\prime}(x)>0$

$\Rightarrow \frac{1}{x \log _{e} a}>0$

For $\log a>1$