| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Simple exponential equation solving |
| Difficulty | Easy -1.2 This question tests basic logarithm laws and simple exponential equation solving using logarithms. Part (i) is straightforward application of log addition (log 5 + log 1.6 = log 8 = 3), and part (ii) is a standard textbook exercise requiring taking logs of both sides. Both parts are routine recall with minimal problem-solving, making this easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\log_2 5 + \log_2 1.6 = \log_2 5 \times 1.6\) | M1 | |
| \(= \log_2 8 = 3\) | A1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2^x = 3 \Rightarrow x\ln 2 = \ln 3\) | M1 | |
| \(\Rightarrow x = \frac{\ln 3}{\ln 2}\) | A1 | |
| \(\approx 1.5850\) | A1 | [3] |
## Question 2:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\log_2 5 + \log_2 1.6 = \log_2 5 \times 1.6$ | M1 | |
| $= \log_2 8 = 3$ | A1 | **[2]** |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2^x = 3 \Rightarrow x\ln 2 = \ln 3$ | M1 | |
| $\Rightarrow x = \frac{\ln 3}{\ln 2}$ | A1 | |
| $\approx 1.5850$ | A1 | **[3]** |
---2 (i) Write $\log _ { 2 } 5 + \log _ { 2 } 1.6$ as an integer.\\
(ii) Solve the equation $2 ^ { x } = 3$, giving your answer correct to 4 decimal places.
\hfill \mbox{\textit{OCR MEI C2 Q2 [5]}}