Question 6 - A-Level Maths

AQA AS Paper 2 2021 June — Question 6 3 marks

Exam Board	AQA
Module	AS Paper 2 (AS Paper 2)
Year	2021
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Exponential Equations & Modelling
Type	Simple exponential equation solving
Difficulty	Easy -1.2 This is a straightforward exponential equation requiring only taking logarithms of both sides and applying log laws to rearrange into the required form. It's a routine AS-level technique with no problem-solving or conceptual challenge beyond basic algebraic manipulation.
Spec	1.06g Equations with exponentials: solve a^x = b

6 Find the solution to $$5 ^ { ( 2 x + 4 ) } = 9$$ giving your answer in the form $a + \log _ { 5 } b$, where $a$ and $b$ are integers.

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Question 6:

Answer	Marks	Guidance
Take $\log_5$ of both sides: $2x + 4 = \log_5 9$	M1	Takes logs base 5; condone any base
$2x + 4 = 2\log_5 3$	B1	Writes $\log_n 9$ as $2\log_n 3$
$x = -2 + \log_5 3$	A1	PI by $a = -2$ and $b = 3$

## Question 6:

Take $\log_5$ of both sides: $2x + 4 = \log_5 9$ | M1 | Takes logs base 5; condone any base |
$2x + 4 = 2\log_5 3$ | B1 | Writes $\log_n 9$ as $2\log_n 3$ |
$x = -2 + \log_5 3$ | A1 | PI by $a = -2$ and $b = 3$ |

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6 Find the solution to

$$5 ^ { ( 2 x + 4 ) } = 9$$

giving your answer in the form $a + \log _ { 5 } b$, where $a$ and $b$ are integers.\\

\hfill \mbox{\textit{AQA AS Paper 2 2021 Q6 [3]}}

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Q1 1 Q2 1 Q3 3 Q4 6 Q5 4 Q6 3 Q7 8 Q8 4 Q9 4 Q10 9 Q11 10 Q12 1 Q13 1 Q14 3 Q15 3 Q16 5 Q17 7 Q18 7

Answer	Marks	Guidance
Take \(\log_5\) of both sides: \(2x + 4 = \log_5 9\)	M1	Takes logs base 5; condone any base
\(2x + 4 = 2\log_5 3\)	B1	Writes \(\log_n 9\) as \(2\log_n 3\)
\(x = -2 + \log_5 3\)	A1	PI by \(a = -2\) and \(b = 3\)