CAIE P2 2017 November — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2017
SessionNovember
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 single-step method with no conceptual difficulty beyond basic log laws, making it easier than average but not trivial since it requires algebraic manipulation after applying logs.
Spec1.06g Equations with exponentials: solve a^x = b

1 Use logarithms to solve the equation \(5 ^ { 3 x - 1 } = 2 ^ { 4 x }\), giving your answer correct to 3 significant figures.

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Introduce logarithms to both sides and use power law\*M1
Obtain \((3x-1)\log 5 = 4x\log 2\) or equivalentA1 Allow A1 for poor use of brackets if recovered later
Solve linear equation for \(x\)DM1 dep \*M
Obtain \(0.783\)A1 Allow 3 sf or better
Total4
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| Introduce logarithms to both sides and use power law | \*M1 | |
| Obtain $(3x-1)\log 5 = 4x\log 2$ or equivalent | A1 | Allow A1 for poor use of brackets if recovered later |
| Solve linear equation for $x$ | DM1 | dep \*M |
| Obtain $0.783$ | A1 | Allow 3 sf or better |
| **Total** | **4** | |

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1 Use logarithms to solve the equation $5 ^ { 3 x - 1 } = 2 ^ { 4 x }$, giving your answer correct to 3 significant figures.\\

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