| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log/algebra parts - linked parts (hence) |
| Difficulty | Moderate -0.8 This is a straightforward logarithm manipulation question requiring only standard log laws (product, quotient, power rules) and solving a simple equation. Part (a) and (b) are direct applications of log₂(16) = 4 and basic rules, while part (c) involves combining the expressions and solving a quadratic in a, which is routine for C2 level with no novel problem-solving required. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules |
Given that log₂ x = a, find, in terms of a, the simplest form of
\begin{enumerate}[label=(\alph*)]
\item log₂ (16x), [2]
\item log₂ $\left(\frac{x⁴}{2}\right)$. [3]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Hence, or otherwise, solve
$$\log_2 (16x) - \log_2 \left(\frac{x^4}{2}\right) = \frac{1}{2},$$
giving your answer in its simplest surd form. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [9]}}