| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2017 |
| Session | Specimen |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Identify errors in student work |
| Difficulty | Challenging +1.2 This is a multi-part question testing logarithm laws with some problem-solving required. Part (i) requires finding specific values where incorrect statements happen to be true (moderate algebraic manipulation). Part (ii)(a) is a straightforward proof using change of base. Part (ii)(b) involves base conversion and solving a cubic, but the factorization is relatively standard. While it's an AEA question, the techniques are accessible to strong C3 students with careful workâharder than average but not requiring exceptional insight. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules |
6.(i)Eden,who is confused about the laws of logarithms,states that
$$\left( \log _ { 5 } p \right) ^ { 2 } = \log _ { 5 } \left( p ^ { 2 } \right)$$
and $\log _ { 5 } ( q - p ) = \log _ { 5 } q - \log _ { 5 } p$\\
However,there is a value of $p$ and a value of $q$ for which both statements are correct.\\
Determine these values.\\
(ii)(a)Let $r \in \mathbb { R } ^ { + } , r \neq 1$ .Prove that
$$\log _ { r } A = \log _ { r ^ { 2 } } B \Rightarrow A ^ { 2 } = B$$
(b)Solve
$$\log _ { 4 } \left( 3 x ^ { 3 } + 26 x ^ { 2 } + 40 x \right) = 2 + \log _ { 2 } ( x + 2 )$$
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-20_2261_53_317_1977}
\end{center}
\hfill \mbox{\textit{Edexcel AEA 2017 Q6 [18]}}