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WMA12/01 Jan 2022, Question 4: Solving Exponential and Log Equations

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

The question, in short

Solve log base 3 of (32 − 12x) equals 2 log base 3 of (1 − x) plus 3 using logarithm laws.

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Solution · 5 marks

  1. 12log₃(1 − x) = log₃(1 − x)² and 3 = log₃27
  2. 2log₃(32 − 12x) − log₃(1 − x)² = 3, so log₃[(32 − 12x)/(1 − x)²] = 3
  3. 3(32 − 12x)/(1 − x)² = 27
  4. 432 − 12x = 27(1 − 2x + x²), so 27x² − 42x − 5 = 0
  5. 5(9x + 1)(3x − 5) = 0, so x = −1/9 or x = 5/3
  6. 6x = 5/3 makes 1 − x negative, so reject it: x = −1/9

Answerx = −1/9

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