AQA Paper 2 2024 June — Question 4 3 marks

Exam BoardAQA
ModulePaper 2 (Paper 2)
Year2024
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Equations & Modelling
TypeSimple exponential equation solving
DifficultyModerate -0.8 This is a straightforward logarithmic equation requiring only the standard technique of taking logs of both sides and applying log laws to isolate x. It's a routine procedural question with no conceptual difficulty or problem-solving required, making it easier than average but not trivial since students must correctly manipulate the algebra.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b
Use logarithms to solve the equation $$5^{x-2} = 7^{1570}$$ Give your answer to two decimal places. [3 marks]
Question 4:
AnswerMarks
4Takes logs of both sides to
same base
PI by x−2=log 71570
AnswerMarks Guidance
51.1b B1
5 5
x−2=1570log 7
5
x=2+1570log 7
5
=1900.23
Uses logAn =nlogA
PI by x−2=log 71570
AnswerMarks Guidance
51.1a M1
Completes a reasoned
argument using logarithms to
AnswerMarks Guidance
obtain AWRT 19002.1 R1
Question 4 Total3
QMarking instructions AO 
Question 4:
4 | Takes logs of both sides to
same base
PI by x−2=log 71570
5 | 1.1b | B1 | log ( 5 x−2 ) =log 7 1570
5 5
x−2=1570log 7
5
x=2+1570log 7
5
=1900.23
Uses logAn =nlogA
PI by x−2=log 71570
5 | 1.1a | M1
Completes a reasoned
argument using logarithms to
obtain AWRT 1900 | 2.1 | R1
Question 4 Total | 3
Q | Marking instructions | AO | Marks | Typical solution
Use logarithms to solve the equation
$$5^{x-2} = 7^{1570}$$

Give your answer to two decimal places.
[3 marks]

\hfill \mbox{\textit{AQA Paper 2 2024 Q4 [3]}}
This paper (21 questions)
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Q1 1 Q2 1 Q3 1 Q4 3 Q5 3 Q6 6 Q7 5 Q8 7 Q9 13 Q10 4 Q11 6 Q12 1 Q13 1 Q14 3 Q15 4 Q16 4 Q17 4 Q18 7 Q19 8 Q20 9 Q21 9