CAIE P2 2020 June — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using subtraction law
DifficultyModerate -0.5 This is a straightforward application of logarithm laws (subtraction and power rules) leading to a simple linear equation. It requires only routine manipulation: ln((x+1)/x) = ln(4), then (x+1)/x = 4, solving to x = 1/3. Slightly easier than average due to minimal steps and standard technique.
Spec1.06f Laws of logarithms: addition, subtraction, power rules

1 Solve the equation $$\ln ( x + 1 ) - \ln x = 2 \ln 2$$

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Use correct logarithm property to produce one term on LHSM1
Use correct process to obtain equation without logarithmsM1
Obtain \(\frac{x+1}{x} = 4\) or equivalent and hence \(x = \frac{1}{3}\)A1
Total3
**Question 1:**

| Answer | Mark | Guidance |
|--------|------|----------|
| Use correct logarithm property to produce one term on LHS | M1 | |
| Use correct process to obtain equation without logarithms | M1 | |
| Obtain $\frac{x+1}{x} = 4$ or equivalent and hence $x = \frac{1}{3}$ | A1 | |
| **Total** | **3** | |

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1 Solve the equation

$$\ln ( x + 1 ) - \ln x = 2 \ln 2$$

\hfill \mbox{\textit{CAIE P2 2020 Q1 [3]}}