4MA1/1HR Jun 2020, Question 21: Exponential Equations
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
For the given expression M in terms of n, determine which n values make M equal 2.
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Solution · 5 marks
- 1Write everything in powers of 2 and 3: 18 = 2 × 3², so 18^(4n) = 2^(4n) × 3^(8n)
- 212² = 144 = 2⁴ × 3²
- 3Powers of 2 on the top: 4n + 3(n² − 6n) = 3n² − 14n
- 4Powers of 3 on the top: 8n + 2(1 − 4n) = 2
- 5Dividing by 2⁴ × 3² gives M = 2^(3n² − 14n − 4) × 3⁰ = 2^(3n² − 14n − 4)
- 6M = 2 means 3n² − 14n − 4 = 1, so 3n² − 14n − 5 = 0
- 7Factorise: (3n + 1)(n − 5) = 0
- 8n = −1/3 or n = 5
Answern = −1/3 or n = 5
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