| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Quadratic in exponential form |
| Difficulty | Moderate -0.3 Part (i) is straightforward logarithm evaluation using basic log laws (log₃27 = 3, log₈4 = 2/3). Part (ii) is a standard quadratic-in-disguise problem where 4^x = (2^x)² and the equation becomes y² - 6y = 0, requiring only substitution and factorization. Both parts are routine C2 exercises with no problem-solving insight needed, making this slightly easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
5. (i) Evaluate
$$\log _ { 3 } 27 - \log _ { 8 } 4$$
(ii) Solve the equation
$$4 ^ { x } - 3 \left( 2 ^ { x + 1 } \right) = 0$$
\hfill \mbox{\textit{OCR C2 Q5 [9]}}