CAIE P3 2017 June — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using power law
DifficultyStandard +0.3 This question requires applying logarithm laws to rewrite 2ln x as ln(x²), then exponentiating to get a quadratic equation. It's slightly above average difficulty due to the algebraic manipulation needed, but follows a standard pattern for log equations with no novel insight required.
Spec1.06g Equations with exponentials: solve a^x = b

Solve the equation \(\ln(x^2 + 1) = 1 + 2 \ln x\), giving your answer correct to 3 significant figures. [3]

Question 1:
AnswerMarks Guidance
1Use law of the logarithm of a power or a quotient M1
2+1=ex 2
AnswerMarks
Remove logarithms and obtain a correct equation in x. e.g.xA1
Obtain answer 0.763 and no otherA1
Total:3
Question 1:
1 | Use law of the logarithm of a power or a quotient | M1
2+1=ex 2
Remove logarithms and obtain a correct equation in x. e.g.x | A1
Obtain answer 0.763 and no other | A1
Total: | 3
Solve the equation $\ln(x^2 + 1) = 1 + 2 \ln x$, giving your answer correct to 3 significant figures. [3]

\hfill \mbox{\textit{CAIE P3 2017 Q1 [3]}}