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4PM1/01 Jan 2022, Question 7: The Laws of Logarithms

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks

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The question, in short

Find log base 2 of 16, then use 4 + 2 log base 4 of x = log base 2 of y to show y = 16x and solve a related equation.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

State the value of log base 2 of 16.

  1. 12⁴ = 16, so log₂ 16 = 4

Answer4

Part (b) · 4 marks

Starting from 4 + 2 log base 4 of x = log base 2 of y, show that y equals 16x.

  1. 12 log₄ x = 2 log₂ x / log₂ 4 = log₂ x
  2. 24 = log₂ 16
  3. 3log₂ 16 + log₂ x = log₂ y
  4. 4log₂ 16x = log₂ y, so y = 16x

Answery = 16x shown

Part (c) · 3 marks

Using the earlier result, solve 4 + 2 log base 4 of x = log base 2 of (4x + 5).

  1. 1From (b), with y = 4x + 5: 16x = 4x + 5
  2. 212x = 5
  3. 3x = 5/12

Answerx = 5/12

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