Question:
Prove that the logarithmic function is strictly increasing on $(0, \infty)$.
Solution:
The given function is $f(x)=\log x$.
$\therefore f^{\prime}(x)=\frac{1}{x}$
It is clear that for $x>0, f^{\prime}(x)=\frac{1}{x}>0$.
Hence, $f(x)=\log x$ is strictly increasing in interval $(0, \infty)$.
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