| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.3 Part (i) requires applying logarithm laws to solve for a base, which is slightly less routine than typical log questions. Part (ii) is a standard exponential equation solved by taking logs of both sides. Both are core C2 techniques with straightforward application, making this slightly easier than average but not trivial. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
5. (i) Find the value of $a$ such that
$$\log _ { a } 27 = 3 + \log _ { a } 8$$
(ii) Solve the equation
$$2 ^ { x + 3 } = 6 ^ { x - 1 }$$
giving your answer to 3 significant figures.\\
\hfill \mbox{\textit{OCR C2 Q5 [7]}}