4PM1/02 Jun 2021, Question 8: The Laws of Logarithms
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks
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The question, in short
Solve the pair of simultaneous equations involving log₄ a + 3 log₈ b = 5/2 and 2^a = 16⁴ ÷ 4^(b²) using algebra, finding the values of a and b.
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Solution · 8 marks
- 13 log₈ b = 3 log₄ b / log₄ 8 = 2 log₄ b
- 2log₄ a + 2 log₄ b = 5/2 ⇒ log₄ (ab²) = 5/2 ⇒ ab² = 32
- 32^a = 2^16/2^(2b²) ⇒ a = 16 − 2b²
- 432 = a(8 − a/2) ⇒ a² − 16a + 64 = 0
- 5(a − 8)² = 0 ⇒ a = 8, b² = 4, b = 2 (b > 0 for log₈ b)
Answera = 8, b = 2
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