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4PM1/01 Jan 2020, Question 7: Solving Exponential and Log Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 5 marks

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The question, in short

Solve for x in the equation log base 7 of (8x² − 6x + 3) minus log base 49 of x² equals 3 log base 7 of 2.

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

Solution · 5 marks

  1. 1log₄₉ x² = log₇ x² / log₇ 49 = log₇ x² / 2 = log₇ x
  2. 2log₇ ((8x² − 6x + 3)/x) = log₇ 8
  3. 38x² − 6x + 3 = 8x
  4. 48x² − 14x + 3 = 0
  5. 5(4x − 1)(2x − 3) = 0
  6. 6x = 1/4 or x = 3/2

Answerx = 3/2, x = 1/4

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