| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Solve exponential equation using logarithms |
| Difficulty | Easy -1.2 This is a straightforward two-part question requiring a basic exponential sketch and routine application of logarithms to solve 3^x = 20. Both parts are standard textbook exercises with no problem-solving required—just direct recall and application of logarithm laws. Significantly easier than average A-level questions. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks |
|---|---|
| (i) Correct shape through \((0,1)\), increasing, asymptote at \(y=0\) | B1 B1 |
| (ii) \(x\log 3 = \log 20\) | M1 |
| \(x = \frac{\log 20}{\log 3}\) | M1 |
| \(x = 2.73\) | A1 |
## Question 7:
**(i)** Correct shape through $(0,1)$, increasing, asymptote at $y=0$ | B1 B1 |
**(ii)** $x\log 3 = \log 20$ | M1 |
$x = \frac{\log 20}{\log 3}$ | M1 |
$x = 2.73$ | A1 |
---7 (i) Sketch the graph of $y = 3 ^ { x }$.\\
(ii) Use logarithms to solve the equation $3 ^ { x } = 20$. Give your answer correct to 2 decimal places.
\hfill \mbox{\textit{OCR MEI C2 2007 Q7 [5]}}