| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.3 This is a straightforward logarithm question testing standard laws (power rule, base change) with clear scaffolding in part (a) that directly leads to solving part (b). The algebraic manipulation is routine (2t - t/2 = 4 gives t = 8/3), followed by a simple exponential calculation. Slightly easier than average due to the helpful structure, though it does require multiple logarithm properties. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
5. (a) Given that $t = \log _ { 3 } x$,
\begin{enumerate}[label=(\roman*)]
\item write down an expression in terms of $t$ for $\log _ { 3 } x ^ { 2 }$,
\item show that $\log _ { 9 } x = \frac { 1 } { 2 } t$.\\
(b) Hence, or otherwise, find to 3 significant figures the value of $x$ such that
$$\log _ { 3 } x ^ { 2 } - \log _ { 9 } x = 4$$
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q5 [8]}}