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WMA12/01 Jun 2023, Question 5: Solving Exponential and Log Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 5 marks

The question, in short

Solve log₂(16x) + log₂(x + 1) = 3 + log₂(x + 6) using logarithm laws, showing your working.

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Solution · 5 marks

  1. 1Write 3 = log₂ 8: log₂(16x) + log₂(x + 1) = log₂ 8 + log₂(x + 6)
  2. 2log₂(16x(x + 1)) = log₂(8(x + 6))
  3. 316x² + 16x = 8x + 48
  4. 42x² + x − 6 = 0
  5. 5(2x − 3)(x + 2) = 0, so x = 3/2 or x = −2
  6. 6x = −2 makes log₂(16x) undefined, so x = 3/2 only

Answerx = 3/2

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