NCERT Class 12 · Ch 6 Exercise 6.2 · Q10
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 10
Prove the logarithmic function is increasing on (0,∞).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: Natural log is strictly increasing.
- For x>0, (log x)′=1/x>0.
- The derivative criterion establishes strict increase. More generally log to base B is increasing for B>1; bases 0<B<1 give a decreasing function.
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