4PM1/01R Jun 2020, Question 3: The Laws of Logarithms
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks
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The question, in short
An arithmetic series has nth term ln a + (n − 1) ln b, with a and b positive integers. Given u₂ = ln 12 and u₅ = ln 768, find a and b.
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Solution · 7 marks
- 1u₂: ln 12 = ln a + ln b ⇒ ab = 12
- 2u₅: ln 768 = ln a + 4 ln b ⇒ ab⁴ = 768
- 3Divide: b³ = 768/12 = 64
- 4b = 4, a = 12/4 = 3
Answera = 3, b = 4
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