| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2008 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: one non-log algebraic part |
| Difficulty | Challenging +1.8 Part (i) requires solving a system where incorrect logarithm rules accidentally hold, demanding algebraic manipulation and insight to find p=9, q=27. Part (ii) involves simplifying logarithm expressions, change of base, and solving a cubic equation. Both parts require non-routine problem-solving beyond standard A-level techniques, typical of AEA's challenging nature. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\roman*)]
\item Anna, who is confused about the rules for logarithms, states that
$$(\log_3 p)^2 = \log_3 (p^2)$$
and
$$\log_3(p + q) = \log_3 p + \log_3 q.$$
However, there is a value for $p$ and a value for $q$ for which both statements are correct.
Find the value of $p$ and the value of $q$. [7]
\item Solve
$$\frac{\log_3(3x^3 - 23x^2 + 40x)}{\log_3 9} = 0.5 + \log_3(3x - 8).$$ [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2008 Q5 [14]}}