| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log/algebra parts - simplify/express then solve |
| Difficulty | Moderate -0.8 This is a straightforward application of basic logarithm laws (product, quotient, and power rules) with no problem-solving required. Part (a) is a 'show that' requiring simple manipulation, and part (b) asks for direct application of log laws to isolate y. Both parts are routine textbook exercises testing recall of standard techniques, making this easier than average for A-level. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
5
\begin{enumerate}[label=(\alph*)]
\item Given that
$$\log _ { a } x = 2 \log _ { a } 6 - \log _ { a } 3$$
show that $x = 12$.
\item Given that
$$\log _ { a } y + \log _ { a } 5 = 7$$
express $y$ in terms of $a$, giving your answer in a form not involving logarithms.\\
(3 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2006 Q5 [6]}}