4PM1/01 Jan 2023, Question 9: Solving Exponential and Log Equations
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 8 marks
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The question, in short
Solve the simultaneous equations e^(2y) − x + 2 = 0 and ln(x + 3) − 2y − 1 = 0, giving each value to 2 decimal places.
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Solution · 8 marks
- 1From the first equation: e^(2y) = x − 2
- 2From the second: x + 3 = e^(2y + 1) = e × e^(2y)
- 3x + 3 = e(x − 2)
- 4x(e − 1) = 3 + 2e, x = (3 + 2e)/(e − 1) = 4.91
- 5e^(2y) = x − 2 = 2.909…
- 6y = ½ ln 2.909… = 0.53
Answerx = 4.91, y = 0.53
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