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4PM1/01R Jun 2019, Question 3: Solving Exponential and Log Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks

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The question, in short

Find a logarithm value, then solve a log equation in t > 0, giving the answer as a√b with a and b prime.

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

Part (a) · 1 mark

State the value of log base 3 of 9.

  1. 19 = 3², so log₃ 9 = 2

Answer2

Part (b) · 6 marks

Solve log₃ 9t = log₉ (12/t)² + 2 for t > 0, giving the answer as a√b with a and b prime.

  1. 1log₃ 9 + log₃ t = 2(log₉ 12 − log₉ t) + 2
  2. 2log₉ x = log₃ x/log₃ 9 = ½ log₃ x
  3. 32 + log₃ t = log₃ 12 − log₃ t + 2
  4. 42 log₃ t = log₃ 12 → t² = 12
  5. 5t = √12 = 2√3

Answert = 2√3

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