4MA1/2H Jun 2022, Question 24: Exponential Equations
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Solve 18 × (√27)⁴ⁿ⁺⁶ ÷ (6 × 9²ⁿ⁺⁸) = 3ˣ for x in terms of n, showing clear working and simplifying.
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Solution · 3 marks
- 1Write as powers of 3: √27 = 3^(3/2) and 9 = 3²
- 2(√27)^(4n+6) = 3^(6n+9) and 9^(2n+8) = 3^(4n+16)
- 318 ÷ 6 = 3, so the expression is 3 × 3^(6n+9) ÷ 3^(4n+16)
- 4Add and subtract powers: 1 + 6n + 9 − 4n − 16 = 2n − 6
- 5x = 2n − 6
Answer2n − 6
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