0580/41 May/Jun 2025, Question 21: Exponential Equations
Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 3 marks
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The question, in short
Solve 16^(5m)/4 = 64^(2n) for m, giving the answer as an expression involving n.
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Solution · 3 marks
- 116^(5m) = 4^(2 × 5m) = 4^(10m), so 16^(5m)/4 = 4^(10m − 1)
- 264^(2n) = 4^(3 × 2n) = 4^(6n)
- 310m − 1 = 6n
- 4m = (6n + 1)/10
Answer(6n + 1)/10
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