CAIE P2 2013 June — Question 2 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2013
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using power law
DifficultyStandard +0.3 This is a straightforward logarithm equation requiring application of the power law (2ln x = ln x²) and combining logarithms, followed by solving a simple quadratic. It's slightly above average difficulty due to requiring multiple log laws and algebraic manipulation, but remains a standard textbook exercise with no novel insight needed.
Spec1.06f Laws of logarithms: addition, subtraction, power rules

2 Solve the equation \(\ln ( 3 - 2 x ) - 2 \ln x = \ln 5\).

AnswerMarks Guidance
Use \(2 \ln x = \ln(x^3)\)M1
Use law for addition or subtraction of logarithmsM1
Obtain correct quadratic equation in \(x\)A1
Make reasonable solution attempt at a 3-term quadratic (dependent on previous M marks)DM1
State \(x = \frac{3}{5}\) and no other solutionsA1 [5]
Use $2 \ln x = \ln(x^3)$ | M1 |
Use law for addition or subtraction of logarithms | M1 |
Obtain correct quadratic equation in $x$ | A1 |
Make reasonable solution attempt at a 3-term quadratic (dependent on previous M marks) | DM1 |
State $x = \frac{3}{5}$ and no other solutions | A1 | [5]
2 Solve the equation $\ln ( 3 - 2 x ) - 2 \ln x = \ln 5$.

\hfill \mbox{\textit{CAIE P2 2013 Q2 [5]}}