4PM1/01 Nov 2023, Question 11: The Laws of Logarithms
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks
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The question, in short
Find the values of x and y that satisfy both logarithmic equations 2log₄ x = log₃ 3y² and log₂ x³ + 8log₉ y = 13, showing all steps.
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Solution · 8 marks
- 12log₄ x = 2log₂ x/log₂ 4 = log₂ x
- 2log₃ 3y² = 1 + 2log₃ y, so log₂ x − 2log₃ y = 1
- 3log₂ x³ = 3log₂ x and 8log₉ y = 8log₃ y/log₃ 9 = 4log₃ y
- 43log₂ x + 4log₃ y = 13
- 5Solve: log₂ x = 3 and log₃ y = 1
- 6x = 2³ = 8, y = 3
Answerx = 8, y = 3
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