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WMA12/01 Jun 2024, Question 3: Solving Exponential and Log Equations

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

The question, in short

Solve a logarithmic equation using log laws with full working, then evaluate a log expression in base √a for a positive constant a greater than 1.

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

Part (i) · 5 marks

Use logarithm laws to solve 2 log₂(2 − x) = 4 + log₂(x + 10), showing all stages without relying on a calculator.

  1. 12 log₂(2 − x) = log₂(2 − x)² and 4 = log₂16
  2. 2log₂(2 − x)² = log₂16 + log₂(x + 10) = log₂[16(x + 10)]
  3. 3(2 − x)² = 16(x + 10)
  4. 4x² − 4x + 4 = 16x + 160, so x² − 20x − 156 = 0
  5. 5(x + 6)(x − 26) = 0, so x = −6 or x = 26
  6. 6x = 26 makes 2 − x negative, so reject it: x = −6

Answerx = −6

Part (ii) · 1 mark

Given a positive constant a greater than 1, work out the value of log base √a of a⁶.

  1. 1√a = a^(1/2), so a⁶ = (a^(1/2))¹²
  2. 2log_√a (a⁶) = 12

Answer12

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Also searched as: WMA12 June 2024 · WMA12/01 · wma12 jun24 · IAS Maths Pure Mathematics 2 June 2024 · question 3.
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