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JAMB Mathematics 1982 Question 9

Question 9

Logarithms

Write the equation 2log2 x − xlog2(1 + y) = 3 in a form not involving logarithms.

  1. A.2x − x(1 + y) = 3
  2. B.2x − x(1 + y) = 8
  3. C.x2 = 8(1 + y)x
  4. D.x2 − x(1 + y) = 8
  5. E.x2 − (1 + y)2 = 8x.
Show the answer and explanation

Answer: C (x2 = 8(1 + y)x)

Explanation

2log₂x = log₂x² and xlog₂(1 + y) = log₂(1 + y)ˣ. So log₂[x²/(1 + y)ˣ] = 3, giving x² = 2³(1 + y)ˣ = 8(1 + y)ˣ.