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4PM1/01 Nov 2021, Question 5: Solving Exponential and Log Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks

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The question, in short

Solve log base 3 of √(x − 5) plus log base 9 of (x + 3) minus 1 equals 0, showing clear algebraic working.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Solution · 7 marks

  1. 1log₃ √(x − 5) = (1/2)log₃ (x − 5)
  2. 2log₉ (x + 3) = log₃ (x + 3)/log₃ 9 = (1/2)log₃ (x + 3)
  3. 3(1/2)log₃ (x − 5) + (1/2)log₃ (x + 3) = 1
  4. 4log₃ [(x − 5)(x + 3)] = 2, so (x − 5)(x + 3) = 9
  5. 5x² − 2x − 24 = 0, (x + 4)(x − 6) = 0
  6. 6x = 6 (x = −4 rejected)

Answerx = 6

Stuck on a step? Read the free lesson: Solving Exponential and Log Equations

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