PrepRung
Sign inSign up free

NDA 2023 Maths · Mathematics · Logarithms · hard

The solution set of log 1/2(x-1)>1 is

Single correct option

The solution set of log⁡1/2(x−1)>1\log_{1/2}(x-1)>1 is
  1. A. x>32x>\dfrac32
  2. B. 1<x<321<x<\dfrac32
  3. C. x>1x>1
  4. D. 0<x<320<x<\dfrac32
Show answer and solution

Answer: (B) 1<x<321<x<\dfrac32

The domain requires x>1x>1. Since the base 12\tfrac12 is less than 1, the logarithm is a decreasing function, so the inequality reverses: x−1<(12)1=12x-1<(\tfrac12)^1=\tfrac12. Together, 1<x<321<x<\tfrac32. Option x>32x>\tfrac32 is what results if the reversal is forgotten.
Report a mistake

Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake