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

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Solution

The given function is $f (x) = log x,$ with domain $= (0, \infty)$
$\Rightarrow f^{'} (x) = \frac{1}{x}$
It is clear that for $x > 0$ , $f^{'} (x) = \frac{1}{x} > 0$ .
Hence, $f (x) = log x$ is strictly increasing in interval $(0, \infty)$ .

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