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WMA12/01 Jan 2021, Question 3: The Laws of Logarithms

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks

The question, in short

Solve two logarithmic equations: an exponential equation for x in a specified log form, and a log equation for y using logarithm laws.

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

Part (i) · 3 marks

Solve 7^(x + 2) = 3, giving x = log₇ a with a a rational number in simplest form.

  1. 17^(x + 2) = 7² × 7ˣ = 3
  2. 27ˣ = 3/7² = 3/49
  3. 3x = log₇ (3/49)

Answerx = log₇ (3/49)

Part (ii) · 5 marks

Using logarithm laws, solve 1 + log₂ y + log₂ (y + 4) = log₂ (5 − y).

  1. 1Write 1 as log₂ 2: log₂ 2 + log₂ y + log₂ (y + 4) = log₂ (5 − y)
  2. 2log₂ (2y(y + 4)) = log₂ (5 − y)
  3. 32y(y + 4) = 5 − y
  4. 42y² + 9y − 5 = 0
  5. 5(2y − 1)(y + 5) = 0, so y = 1/2 or y = −5
  6. 6y must be positive for log₂ y, so y = 1/2

Answery = 1/2

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