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UI Post-UTME Mathematics 2024 (Model questions) Question 1

Question 1

Logarithms

Solve the equation: log2(x2 − 5x + 6) = 1

  1. A.x = 1 or 2
  2. B.x = 1 or 4
  3. C.x = 2 or −3
  4. D.x = −1 or 3
Show the answer and explanation

Answer: B (x = 1 or 4)

Explanation

x² − 5x + 6 = 2¹, so x² − 5x + 4 = 0, (x − 1)(x − 4) = 0, x = 1 or 4 (both make the log's argument 2 > 0).