| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Natural logarithm equation solving |
| Difficulty | Moderate -0.3 Part (i) is a straightforward one-step logarithm equation requiring only exponentiation and simple algebra. Part (ii) is more substantial, requiring the substitution u = e^y to form a quadratic equation, then solving and taking logarithms, but this is a standard C3 technique. Overall slightly easier than average due to the routine nature of both parts, though (ii) provides some modest challenge. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
2. Solve each equation, giving your answers in exact form.\\
(i) $\quad \ln ( 2 x - 3 ) = 1$\\
(ii) $3 \mathrm { e } ^ { y } + 5 \mathrm { e } ^ { - y } = 16$\\
\hfill \mbox{\textit{OCR C3 Q2 [7]}}