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4PM1/02 Jun 2020, Question 4: Solving Exponential and Log Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 marks

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The question, in short

Find the value of r that satisfies a logarithmic equation, then find x from a second equation combining several base-5 logs with powers of x.

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

Part (i) · 2 marks

Determine r so that 16 times log base r of 4 equals log base 4 of r.

  1. 1log_r 4 = 1/log₄ r
  2. 216/log₄ r = log₄ r ⇒ (log₄ r)² = 16
  3. 3log₄ r = ±4
  4. 4r = 4⁴ = 256 or r = 4⁻⁴ = 1/256

Answerr = 256 or r = 1/256

Part (ii) · 5 marks

Determine x so that the sum of four base-5 logs of 9, 12, 15 and 18 equals 1 plus logs of x and x².

  1. 1LHS = log₅(9 × 12 × 15 × 18) = log₅ 29160
  2. 2RHS = log₅ 5 + log₅ x + log₅ x² = log₅ 5x³
  3. 35x³ = 29160 ⇒ x³ = 5832
  4. 4x = 18

Answerx = 18

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

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