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NDA 1 2024 Maths, question 27

Topic: Algebra

Q27

What is the number of solutions of log⁡4(x−1)=log⁡2(x−3)\log _{4}(x-1)=\log _{2}(x-3) ?

  1. (a) Zero
  2. (b) OneCorrect answer
  3. (c) Two
  4. (d) Three

Solution.

Answer: (b) One

  1. The logarithm domain requires x>3.
  2. Change base to obtain log₂(x−1)=2log₂(x−3), so x−1=(x−3)².
  3. Thus x²−7x+10=(x−5)(x−2)=0.
  4. Only x=5 satisfies the domain, giving one solution.