| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log/algebra parts - simplify/express then solve |
| Difficulty | Easy -1.2 This is a straightforward application of basic logarithm laws (subtraction rule, power rule, and the fact that log_a(a)=1). Part (a) requires one step of recall, part (b) requires combining three standard rules but involves no problem-solving or insight beyond direct application of memorized formulas. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(x = 8\) | B1 | No clear log law errors seen. Condone answer left as \(\frac{16}{2}\) — Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(\log_a y = \log_a 3^2 + \log_a 4 + 1\) | M1 | One law of logs used correctly |
| \(\log_a y = \log_a(3^2\times 4)+1\) | M1 | Either a second law of logs used correctly or the 1 written as \(\log_a a\) |
| \(\log_a y = \log_a(3^2\times 4) + \log_a a = \log_a 36a\) | ||
| \(\Rightarrow y = 36a\) | A1 | CSO — Total: 3 |
## Question 7:
### Part (a)
| Working | Mark | Guidance |
|---------|------|----------|
| $x = 8$ | B1 | No clear log law errors seen. Condone answer left as $\frac{16}{2}$ — **Total: 1** |
### Part (b)
| Working | Mark | Guidance |
|---------|------|----------|
| $\log_a y = \log_a 3^2 + \log_a 4 + 1$ | M1 | One law of logs used correctly |
| $\log_a y = \log_a(3^2\times 4)+1$ | M1 | Either a second law of logs used correctly or the 1 written as $\log_a a$ |
| $\log_a y = \log_a(3^2\times 4) + \log_a a = \log_a 36a$ | | |
| $\Rightarrow y = 36a$ | A1 | CSO — **Total: 3** |7
\begin{enumerate}[label=(\alph*)]
\item Given that
$$\log _ { a } x = \log _ { a } 16 - \log _ { a } 2$$
write down the value of $x$.
\item Given that
$$\log _ { a } y = 2 \log _ { a } 3 + \log _ { a } 4 + 1$$
express $y$ in terms of $a$, giving your answer in a form not involving logarithms.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2008 Q7 [4]}}