4PM1/02 Jun 2022, Question 10: The Laws of Logarithms
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks
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The question, in short
Solve log base 4 of x plus log base 16 of x plus log base 2 of x equals 10.5, showing clear working.
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Solution · 5 marks
- 1log₄ x = log₂ x/log₂ 4 = (log₂ x)/2, log₁₆ x = (log₂ x)/4
- 2(1/2)log₂ x + (1/4)log₂ x + log₂ x = 10.5
- 3(7/4)log₂ x = 10.5 ⇒ log₂ x = 6
- 4x = 2⁶ = 64
Answerx = 64
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