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Prove that the logarithmic function is strictly increasing on $(0, \infty)$
MathematicsApplication of Derivatives
Solution:
1338 Upvotes Verified Answer
Let $\mathrm{f}(\mathrm{x})=\log \mathrm{x}$ Now, $\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{\mathrm{x}}$; When takes the values $\mathrm{x}>0$, $\frac{1}{x}>0$, when $x>0, \because f^{\prime}(x)>0$
Hence, $\mathrm{f}(\mathrm{x})$ is an increasing function for $\mathrm{x}>0$ i.e.

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