CAIE P2 2017 June — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward exponential equation requiring only the standard technique of taking logarithms of both sides and rearranging to solve for x. It's a routine textbook exercise with no problem-solving insight needed, making it easier than average, though not trivial since it requires correct algebraic manipulation of logarithms.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
2 Use logarithms to solve the equation \(3 ^ { x + 4 } = 5 ^ { 2 x }\), giving your answer correct to 3 significant figures.
Question 2:
AnswerMarks Guidance
AnswerMark Guidance
Apply logarithms to both sides and apply power law\*M1
Obtain \((x+4)\log 3 = 2x\log 5\) or equivalentA1
Solve linear equation for \(x\)DM1 dep \*M
Obtain 2.07A1 Allow greater accuracy
Total:4 
## Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| Apply logarithms to both sides and apply power law | \*M1 | |
| Obtain $(x+4)\log 3 = 2x\log 5$ or equivalent | A1 | |
| Solve linear equation for $x$ | DM1 | dep \*M |
| Obtain 2.07 | A1 | Allow greater accuracy |
| **Total:** | **4** | |

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2 Use logarithms to solve the equation $3 ^ { x + 4 } = 5 ^ { 2 x }$, giving your answer correct to 3 significant figures.\\

\hfill \mbox{\textit{CAIE P2 2017 Q2 [4]}}
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Q1 3 Q2 4 Q3 5 Q4 5 Q5 6 Q6 7 Q7 9 Q8 11