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WMA12/01 Jan 2023, Question 4: Solving Exponential and Log Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Solve two logarithm problems: one equation in x using log laws, and one summation identity to express y in terms of a in simplest form.

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

Part (i) · 3 marks

Apply logarithm laws to solve log base 3 of 4x plus 2 equals log base 3 of 5x plus 7 for x.

  1. 12 = log₃ 9, so log₃(4x) + log₃ 9 = log₃(5x + 7)
  2. 2log₃(36x) = log₃(5x + 7)
  3. 336x = 5x + 7 ⇒ 31x = 7
  4. 4x = 7/31

Answerx = 7/31

Part (ii) · 3 marks

Given a sum of log base a of y to the r equals a sum of powers of log base a of y for r from 1 to 2, find y in terms of a.

  1. 1Left side: logₐ y + logₐ y² = 3 logₐ y
  2. 2Right side: logₐ y + (logₐ y)²
  3. 33 logₐ y = logₐ y + (logₐ y)² ⇒ logₐ y(2 − logₐ y) = 0
  4. 4y > 1 so logₐ y ≠ 0, hence logₐ y = 2
  5. 5y = a²

Answery = a²

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Also searched as: WMA12 January 2023 · WMA12/01 · wma12 jan23 · IAS Maths Pure Mathematics 2 January 2023 · question 4.
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