| 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 - simplify/express then solve |
| Difficulty | Moderate -0.8 Part (i) is a straightforward application of log laws (addition/subtraction rules) requiring only algebraic manipulation to reach log₃(25) = 2. Part (ii) involves rearranging an exponential equation using log laws, which is routine C2 material. Both parts test standard techniques with no problem-solving insight required, making this easier than average but not trivial. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules |
\begin{enumerate}[label=(\roman*)]
\item Evaluate $\log_3 15 + \log_3 20 - \log_3 12$. [3]
\item Given that $y = 3 \times 10^{2x}$, show that $x = a \log_{10}(by)$, where the values of the constants $a$ and $b$ are to be found. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q7 [7]}}