Question 4 - A-Level Maths

AQA C2 2013 January — Question 4 3 marks

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2013
Session	January
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Laws of Logarithms
Type	Solve ln equation using subtraction law
Difficulty	Moderate -0.8 This is a straightforward application of logarithm laws requiring only two steps: combine logs using the subtraction rule (log A - log B = log(A/B)), then convert to exponential form. It's routine manipulation with no problem-solving insight needed, making it easier than average but not trivial since it requires knowing both laws.
Spec	1.06f Laws of logarithms: addition, subtraction, power rules

4 Given that $$\log _ { a } N - \log _ { a } x = \frac { 3 } { 2 }$$ express $x$ in terms of $a$ and $N$, giving your answer in a form not involving logarithms.
(3 marks)

Show mark scheme Show mark scheme source

Question 4:

Answer	Marks	Guidance
Working	Marks	Guidance
$\log_a N - \log_a x = \frac{3}{2}$
$\log_a \frac{N}{x} = \frac{3}{2}$	M1	A log law used correctly. PI by next line
$\frac{N}{x} = a^{\frac{3}{2}}$	m1	Logarithm(s) eliminated correctly
$x = a^{-\frac{3}{2}}N$	A1	ACF of RHS
Total: 3 marks

# Question 4:
| Working | Marks | Guidance |
|---------|-------|----------|
| $\log_a N - \log_a x = \frac{3}{2}$ | | |
| $\log_a \frac{N}{x} = \frac{3}{2}$ | M1 | A log law used correctly. PI by next line |
| $\frac{N}{x} = a^{\frac{3}{2}}$ | m1 | Logarithm(s) eliminated correctly |
| $x = a^{-\frac{3}{2}}N$ | A1 | ACF of RHS |
| **Total: 3 marks** | | |

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4 Given that

$$\log _ { a } N - \log _ { a } x = \frac { 3 } { 2 }$$

express $x$ in terms of $a$ and $N$, giving your answer in a form not involving logarithms.\\
(3 marks)

\hfill \mbox{\textit{AQA C2 2013 Q4 [3]}}

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Q1 5 Q2 9 Q3 6 Q4 3 Q5 12 Q6 10 Q7 9 Q8 9 Q9 12