| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: both solve equations |
| Difficulty | Standard +0.3 Part (i) requires standard logarithm manipulation (bringing terms to one side, using log laws, solving a quadratic) which is routine C2 content. Part (ii) involves taking logarithms of both sides and rearranging, which is straightforward once the technique is recognized. Both parts are textbook-style exercises with no novel insight required, making this 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=(\roman*)]
\item Solve the equation
$$\log_2 (6 - x) = 3 - \log_2 x.$$ [4]
\item Find the smallest integer $n$ such that
$$3^{n-2} > 8^{250}.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q5 [8]}}