4PM1/02R Jun 2024, Question 6: Exponentials, Logarithms, e and ln
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 7 marks
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The question, in short
Use the given graph of y = x + 2^(−(4x+1)) and a suitable straight line to estimate, to one decimal place, the roots of log₂(8 − 3x) + 4x = 0 for −2 ≤ x ≤ 6.
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Solution · 7 marks
- 1log₂(8 − 3x) = −4x, so 8 − 3x = 2^(−4x)
- 2Divide by 2: 4 − (3/2)x = 2^(−4x − 1)
- 3Add x to both sides: 4 − x/2 = x + 2^(−(4x+1))
- 4Draw the line y = 4 − x/2
- 5Intersections give x ≈ −0.8 and x ≈ 2.7
Answerx = −0.8 (or −0.9) and x = 2.6 (or 2.7)
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