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0606/11 May/Jun 2025, Question 8: Solving Exponential and Log Equations

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Find where log base 5 of 12x − 4 is defined, then solve log₅(12x − 4) = 6/(logₓ 125) + 1.

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Part (a) · 1 mark

State the range of x values for which log₅(12x − 4) is defined.

  1. 1Need 12x − 4 > 0
  2. 2x > 4/12 = 1/3

Answerx > 1/3

Part (b) · 6 marks

Solve log₅(12x − 4) = 6/(logₓ 125) + 1 for x.

  1. 1logₓ 125 = log₅ 125/log₅ x = 3/log₅ x
  2. 26/(logₓ 125) = 2log₅ x
  3. 3log₅(12x − 4) = 2log₅ x + 1
  4. 4log₅((12x − 4)/x²) = 1, so 12x − 4 = 5x²
  5. 55x² − 12x + 4 = 0
  6. 6(5x − 2)(x − 2) = 0, so x = 0.4 or x = 2

Answerx = 0.4, 2

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Also searched as: 0606/11/M/J/25 · 0606_s25_qp_11 · 0606 s25 11 · question 8.
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