Question 1 - A-Level Maths

CAIE P2 2015 November — Question 1 4 marks

Exam Board	CAIE
Module	P2 (Pure Mathematics 2)
Year	2015
Session	November
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Exponential Equations & Modelling
Type	Simple exponential equation solving
Difficulty	Moderate -0.8 This is a straightforward application of logarithms to solve an exponential equation with a single unknown. It requires taking logs of both sides, expanding using log laws, collecting terms in x, and calculator work—all standard techniques with no problem-solving insight needed. Simpler than average A-level questions due to being purely procedural with one clear method.
Spec	1.06g Equations with exponentials: solve a^x = b

1 Use logarithms to solve the equation $$5 ^ { x + 3 } = 7 ^ { x - 1 }$$ giving the answer correct to 3 significant figures.

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Answer	Marks	Guidance
Introduce logarithms and use power law twice. Obtain $(x + 3) \log 5 = (x - 1) \log 7$ or equivalent	M1* A1
Solve linear equation for $x$. Obtain $20.1$	M1 dep A1	[4]

Introduce logarithms and use power law twice. Obtain $(x + 3) \log 5 = (x - 1) \log 7$ or equivalent | M1* A1 |
Solve linear equation for $x$. Obtain $20.1$ | M1 dep A1 | [4]

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1 Use logarithms to solve the equation

$$5 ^ { x + 3 } = 7 ^ { x - 1 }$$

giving the answer correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P2 2015 Q1 [4]}}

This paper (7 questions)

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Q1 4 Q2 5 Q3 7 Q4 7 Q5 7 Q6 9 Q7 11

Answer	Marks	Guidance
Introduce logarithms and use power law twice. Obtain \((x + 3) \log 5 = (x - 1) \log 7\) or equivalent	M1* A1
Solve linear equation for \(x\). Obtain \(20.1\)	M1 dep A1	[4]