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4PM1/01 Jun 2025, Question 10: Solving Exponential and Log Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 11 marks

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The question, in short

Solve two logarithmic equations, showing algebraic working; give the second answer to 3 significant figures.

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

Part (i) · 2 marks

Solve log base 4 of (6y − 5) equals 3 for y.

  1. 16y − 5 = 4³ = 64
  2. 2y = 69/6 = 23/2

Answery = 23/2

Part (ii) · 9 marks

Solve log base 4 of (4 − 3x)² minus log base 2 of (x² − 5) minus 3 equals 0, to 3 significant figures.

  1. 1log₂(x² − 5) = log₄(x² − 5)/log₄ 2 = 2 log₄(x² − 5)
  2. 2Divide by 2: log₄(4 − 3x) − log₄(x² − 5) = 3/2
  3. 3(4 − 3x)/(x² − 5) = 4^(3/2) = 8
  4. 48x² + 3x − 44 = 0
  5. 5x = (−3 ± √1417)/16 = 2.165… or −2.540…
  6. 6x = 2.165 makes x² − 5 < 0, so x = −2.54

Answerx = −2.54

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