| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Natural logarithm equation solving |
| Difficulty | Moderate -0.8 This is a straightforward question testing basic logarithm and exponential manipulation. Part (i) requires a single application of natural logarithm, while part (ii) involves standard log laws and solving a linear equation. Both are routine exercises with no problem-solving insight required, making this easier than average for C3. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
Solve each equation, giving your answers in exact form.
\begin{enumerate}[label=(\roman*)]
\item $\mathrm{e}^{4x-3} = 2$ [2]
\item $\ln(2y - 1) = 1 + \ln(3 - y)$ [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q4 [6]}}