CAIE P2 2017 November — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionNovember
Marks4
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Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using subtraction law
DifficultyModerate -0.3 This is a straightforward application of the logarithm subtraction law (ln a - ln b = ln(a/b)) followed by exponentiating both sides and solving a linear equation. It's slightly easier than average as it requires only one standard technique and basic algebraic manipulation, with no conceptual challenges or multi-step problem-solving.
Spec1.06g Equations with exponentials: solve a^x = b
1 Solve the equation \(\ln ( 3 x + 1 ) - \ln ( x + 2 ) = 1\), giving your answer in terms of e.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Use subtraction or addition property of logarithms\*M1
Obtain \(\frac{3x+1}{x+2} = e\) or equivalent with no presence of logarithmA1
Use correct process to solve equationDM1
Obtain \(\frac{2e-1}{3-e}\) or exact equivalentA1 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use subtraction or addition property of logarithms | \*M1 | |
| Obtain $\frac{3x+1}{x+2} = e$ or equivalent with no presence of logarithm | A1 | |
| Use correct process to solve equation | DM1 | |
| Obtain $\frac{2e-1}{3-e}$ or exact equivalent | A1 | |

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1 Solve the equation $\ln ( 3 x + 1 ) - \ln ( x + 2 ) = 1$, giving your answer in terms of e.\\

\hfill \mbox{\textit{CAIE P2 2017 Q1 [4]}}
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