4PM1/01 Jun 2023, Question 6: Solving Exponential and Log Equations
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks
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The question, in short
Solve log₂ x³ + log₄ x² − 3 log_x 2 = 0, giving answers to 3 significant figures.
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Solution · 8 marks
- 1log₄ x² = log₂ x²/log₂ 4 = 2log₂ x/2 = log₂ x
- 23 log_x 2 = 3/log₂ x
- 33log₂ x + log₂ x − 3/log₂ x = 0
- 4Multiply by log₂ x: 4(log₂ x)² = 3
- 5log₂ x = ±√(3/4)
- 6x = 2^(√3/2) ≈ 1.82 or x = 2^(−√3/2) ≈ 0.549
Answerx = 1.82 or x = 0.549
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