0606/23 May/Jun 2025, Question 13: Solving Exponential and Log Equations
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 4 marks
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The question, in short
Solve the equation 64^(x + 1/3) + 2^(3x) − 3 = 0 for x.
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Solution · 4 marks
- 164^(x + 1/3) = 64^(1/3) × 64^x = 4 × 8^(2x)
- 2Let u = 8^x: 4u² + u − 3 = 0
- 3(4u − 3)(u + 1) = 0
- 4u = 3/4 (8^x = −1 has no solution)
- 5x = log₈ 0.75 ≈ −0.138
Answerx = log₈ 0.75 = (1/3) log₂ 0.75 = −0.138
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Also searched as: 0606/23/M/J/25 · 0606_s25_qp_23 · 0606 s25 23 · question 13.
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