CAIE P3 2024 June — Question 2 4 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2024
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLaws of Logarithms
TypeSolve ln equation using subtraction law
DifficultyStandard +0.3 This question requires applying the logarithm subtraction law to combine terms, then exponentiating and solving a quadratic equation. While it involves multiple steps (rearranging, using log laws, exponentiating, quadratic formula), these are all standard techniques that students practice regularly. The algebraic manipulation is straightforward with no conceptual surprises, making it slightly easier than average.
Spec1.06g Equations with exponentials: solve a^x = b

2 Solve the equation \(\ln ( x - 5 ) = 7 - \ln x\). Give your answer correct to 2 decimal places.

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Use law of logarithm of a product (or quotient) on correct terms\*M1
Use correct method to eliminate logarithmDM1
Obtain a correct quadratic in \(x\), e.g. \(x^2-5x-e^7=0\) (allow decimals)A1
Obtain answer \(x=35.71\) onlyA1
Total4
**Question 2:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use law of logarithm of a product (or quotient) on correct terms | \*M1 | |
| Use correct method to eliminate logarithm | DM1 | |
| Obtain a correct quadratic in $x$, e.g. $x^2-5x-e^7=0$ (allow decimals) | A1 | |
| Obtain answer $x=35.71$ only | A1 | |
| **Total** | **4** | |
2 Solve the equation $\ln ( x - 5 ) = 7 - \ln x$. Give your answer correct to 2 decimal places.\\

\hfill \mbox{\textit{CAIE P3 2024 Q2 [4]}}