Lemmara logoLemmaraWorked solution

WMA12/01 Jun 2022, Question 4: Solving Exponential and Log Equations

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

The question, in short

Given positive constants a and b, solve the simultaneous equations a − b = 8 and log₄ a + log₄ b = 3, giving answers in fully simplified surd form.

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

Solution · 6 marks

  1. 1log₄ a + log₄ b = log₄(ab) = 3, so ab = 4³ = 64
  2. 2a = b + 8, so (b + 8)b = 64
  3. 3b² + 8b − 64 = 0
  4. 4b = (−8 ± √(64 + 256))/2 = (−8 ± 8√5)/2 = −4 ± 4√5
  5. 5b > 0, so b = −4 + 4√5
  6. 6a = b + 8 = 4 + 4√5

Answera = 4 + 4√5, b = −4 + 4√5

Stuck on a step? Read the free lesson: Solving Exponential and Log Equations

Practise more solving exponential and log equations questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on solving exponential and log equations

Also searched as: WMA12 June 2022 · WMA12/01 · wma12 jun22 · IAS Maths Pure Mathematics 2 June 2022 · question 4.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.