| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log/algebra parts - linked parts (hence) |
| Difficulty | Moderate -0.3 This is a straightforward logarithm manipulation question testing standard log laws (quotient, power, and root rules). Part (a) requires direct application of log rules with substitution, while part (b) involves combining these to solve a linear equation in y. The question is slightly easier than average as it's highly structured with clear guidance ('hence') and uses only basic log properties without requiring creative problem-solving. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
\begin{enumerate}[label=(\alph*)]
\item Given that $y = \log_2 x$, find expressions in terms of $y$ for
\begin{enumerate}[label=(\roman*)]
\item $\log_2 \left(\frac{x}{2}\right)$, [2]
\item $\log_2 (\sqrt{x})$. [2]
\end{enumerate}
\item Hence, or otherwise, solve the equation
$$2 \log_2 \left(\frac{x}{2}\right) + \log_2 (\sqrt{x}) = 8.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q4 [7]}}