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0606/13 May/Jun 2025, Question 6: Solving Exponential and Log Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Find exact x-coordinates where y = 4ln x meets y = 5 − 3/ln(x²).

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Solution · 5 marks

  1. 1ln(x²) = 2ln x, so 4ln x = 5 − 3/(2ln x)
  2. 2Multiply by 2ln x: 8(ln x)² = 10ln x − 3
  3. 38(ln x)² − 10ln x + 3 = 0
  4. 4(4ln x − 3)(2ln x − 1) = 0
  5. 5ln x = 0.75 or ln x = 0.5
  6. 6x = e^0.75 or x = e^0.5

Answerx = e^0.75, x = e^0.5

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Also searched as: 0606/13/M/J/25 · 0606_s25_qp_13 · 0606 s25 13 · question 6.
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