| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve by showing reduces to polynomial |
| Difficulty | Moderate -0.3 This is a straightforward C2 logarithm question requiring standard manipulation of log laws (part a), solving a quadratic equation (part b), and simple substitution (parts c-d). While multi-part, each step follows directly from the previous with no novel insight required, making it slightly easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\alph*)]
\item Given that $3 + 2 \log_2 x = \log_2 y$, show that $y = 8x^2$. [3]
\item Hence, or otherwise, find the roots $\alpha$ and $\beta$, where $\alpha < \beta$, of the equation
$$3 + 2 \log_2 x = \log_2 (14x - 3).$$ [3]
\item Show that $\log_2 \alpha = -2$. [1]
\item Calculate $\log_2 \beta$, giving your answer to 3 significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q28 [10]}}