Ex 6.2, 10 - Prove logarithmic function is strictly increasing - To show increasing/decreasing in whole domain

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Ex 6.2,10 Prove that the logarithmic function is strictly increasing on (0, 𕔴). f﷐𝑥﷯ = log ﷐𝑥﷯ We need to prove f﷐𝑥﷯ in increasing on 𝑥 ∈ ﷐0 , 𕔴uc1﷯ i.e. we need to show f’ ﷐𝑥﷯ > 0 for x ∈ ﷐0 , 𕔴uc1﷯ Now, f ﷐𝑥﷯ = log 𝑥 f’﷐𝑥﷯ = ﷐1﷮𝑥﷯ When 𝑥 > 0 ⇒ ﷐1 ﷮𝑥﷯ > 0 ⇒ f’﷐𝑥﷯ > 0 Hence f﷐𝑥﷯ is an increasing function for 𝒙 > 0

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