Question 1 - A-Level Maths

CAIE P2 2016 June — Question 1 3 marks

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2016
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Exponential Equations & Modelling
Type	Exponential to linear form proof
Difficulty	Moderate -0.8 This is a straightforward logarithmic manipulation question requiring only the application of log laws to both sides and simple algebraic rearrangement. It's a standard textbook exercise with a single clear method and no problem-solving insight required, making it easier than average.
Spec	1.06f Laws of logarithms: addition, subtraction, power rules 1.06g Equations with exponentials: solve a^x = b

1 Given that \(5 ^ { 3 x } = 7 ^ { 4 y }\), use logarithms to find the value of \(\frac { x } { y }\) correct to 4 significant figures.

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Question 1:

Answer	Marks	Guidance
Answer/Working	Mark	Guidance
Use power law for logarithms correctly at least once	M1
Obtain \(3x\log 5 = 4y\log 7\) or \(3x\ln 5 = 4y\ln 7\) or equivalent	A1
Obtain 1.612	A1	[3]

## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use power law for logarithms correctly at least once | M1 | |
| Obtain $3x\log 5 = 4y\log 7$ or $3x\ln 5 = 4y\ln 7$ or equivalent | A1 | |
| Obtain 1.612 | A1 | [3] |

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1 Given that $5 ^ { 3 x } = 7 ^ { 4 y }$, use logarithms to find the value of $\frac { x } { y }$ correct to 4 significant figures.

\hfill \mbox{\textit{CAIE P2 2016 Q1 [3]}}

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Q1 3 Q2 5 Q3 5 Q4 8 Q5 9 Q6 10 Q7 10