CAIE P2 2011 November — Question 3 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2011
SessionNovember
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 standard log laws (power law and subtraction law) to combine terms, then solving the resulting algebraic equation. It's slightly above average difficulty due to requiring multiple steps and careful algebraic manipulation, but follows a standard textbook pattern with no novel insight needed.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b

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

AnswerMarks Guidance
Use \(2 \ln(x + 3) = \ln(x + 3)^2\)M1
Use law for addition or subtraction of logarithmsM1
Obtain correct quadratic expression in \(x\)A1
Make reasonable solution attempt at a 3-term quadraticM1
State \(x = 9\) and no other solutions (condone \(x = -1\) not deleted)A1 [5]
Use $2 \ln(x + 3) = \ln(x + 3)^2$ | M1 |
Use law for addition or subtraction of logarithms | M1 |
Obtain correct quadratic expression in $x$ | A1 |
Make reasonable solution attempt at a 3-term quadratic | M1 |
State $x = 9$ and no other solutions (condone $x = -1$ not deleted) | A1 | [5]
3 Solve the equation $2 \ln ( x + 3 ) - \ln x = \ln ( 2 x - 2 )$.

\hfill \mbox{\textit{CAIE P2 2011 Q3 [5]}}