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WMA12/01 Oct 2020, Question 9: Solving Exponential and Log Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 10 marks

The question, in short

Solve a logarithmic equation exactly for x, then use powers to derive an exponential relation and find y to 3 decimal places.

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

Part (i) · 4 marks

Find the exact x satisfying log base 3 of (x + 5) minus 4 equals log base 3 of (2x − 1).

  1. 14 = log₃81
  2. 2log₃(x + 5) − log₃(2x − 1) = 4, so log₃((x + 5)/(2x − 1)) = 4
  3. 3(x + 5)/(2x − 1) = 3⁴ = 81
  4. 4x + 5 = 162x − 81, so 161x = 86
  5. 5x = 86/161

Answerx = 86/161

Part (iia) · 4 marks

Starting from 3^(y+3) × 2^(1−2y) = 108, show that 0.75^y = 2.

  1. 13^(y+3) = 27 × 3ʸ and 2^(1−2y) = 2 × 2⁻²ʸ = 2/4ʸ
  2. 227 × 3ʸ × 2/4ʸ = 108
  3. 33ʸ/4ʸ = 108/54 = 2
  4. 4(3/4)ʸ = 2, so 0.75ʸ = 2

AnswerShown: 27 × 3ʸ × 2 × 2⁻²ʸ = 108, so 3ʸ/4ʸ = 2, i.e. 0.75ʸ = 2

Part (iib) · 2 marks

Using 0.75^y = 2, calculate y rounded to 3 decimal places.

  1. 1y = log 2 / log 0.75
  2. 2y = −2.409 (3 d.p.)

Answery = −2.409

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

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