4PM1/02R Jun 2023, Question 10: Solving Exponential and Log Equations
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 7 marks
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The question, in short
Solve the logarithmic equation log₄ x³ + 8 log_x 64 = 22 for x, showing valid solutions.
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Solution · 7 marks
- 18 log_x 64 = 8 log₄ 64/log₄ x = 24/log₄ x
- 2log₄ x³ = 3 log₄ x
- 33 log₄ x + 24/log₄ x = 22
- 43(log₄ x)² − 22 log₄ x + 24 = 0
- 5(3 log₄ x − 4)(log₄ x − 6) = 0, so log₄ x = 4/3 or 6
- 6x = 4^(4/3) ≈ 6.35 or x = 4⁶ = 4096
Answerx = 4^(4/3) (≈ 6.35) and x = 4096
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