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WMA12/01 Oct 2022, Question 10: Solving Exponential and Log Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Using a = log₂3, express two logarithmic quantities in terms of a, then solve an equation in x involving 3ˣ and 2ˣ⁺⁴, giving x in terms of a.

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

Part (ia) · 1 mark

Express log₂9 using a only, in its simplest form.

  1. 1log₂9 = log₂3²
  2. 2= 2log₂3 = 2a

Answer2a

Part (ib) · 2 marks

Express log₂(√3/16) in terms of a, simplified as far as possible.

  1. 1log₂(√3/16) = log₂√3 − log₂16
  2. 2= (1/2)log₂3 − 4
  3. 3= (1/2)a − 4

Answer(1/2)a − 4

Part (ii) · 4 marks

Find x satisfying 3ˣ × 2ˣ⁺⁴ = 6, with the answer in simplest form involving a.

  1. 1Take log₂ of both sides: log₂3ˣ + log₂2ˣ⁺⁴ = log₂6
  2. 2x log₂3 + (x + 4) = log₂2 + log₂3
  3. 3ax + x + 4 = 1 + a
  4. 4x(a + 1) = a − 3
  5. 5x = (a − 3)/(a + 1)

Answerx = (a − 3)/(a + 1)

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Also searched as: WMA12 October 2022 · WMA12/01 · wma12 oct22 · IAS Maths Pure Mathematics 2 October 2022 · question 10.
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