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Prove that the Logarithmic Function is Strictly Increasing on (0, ∞). - CBSE (Commerce) Class 12 - Mathematics

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Question

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

Solution

The given function is f(x) =  logx

`:. f'(x) = 1/x`

It is clear that for x > 0,  `f'(x) = 1/x > 0`

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

 

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 6: Application of Derivatives
Q: 10 | Page no. 206
Solution Prove that the Logarithmic Function is Strictly Increasing on (0, ∞). Concept: Increasing and Decreasing Functions.
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