| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Expand single log into combination |
| Difficulty | Easy -1.2 This question tests basic logarithm laws (power rule and addition rule) with straightforward algebraic manipulation. Part (i) is direct application of log laws requiring no problem-solving, and part (ii) is a simple rearrangement. Both parts are routine textbook exercises with minimal steps, making this easier than average for A-level. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| \(\log_a x^4 + \log_a x^{-1} = \log_a x^3 = 3\log_a x\) | M1 A1 | Using log laws correctly; \(3\log_a x\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\log_{10}(bc) = 3\) | M1 | Using addition log law |
| \(bc = 1000\), so \(b = \frac{1000}{c}\) | A1 | cao |
## Question 10(i):
$\log_a x^4 + \log_a x^{-1} = \log_a x^3 = 3\log_a x$ | M1 A1 | Using log laws correctly; $3\log_a x$
## Question 10(ii):
$\log_{10}(bc) = 3$ | M1 | Using addition log law
$bc = 1000$, so $b = \frac{1000}{c}$ | A1 | cao
---10 (i) Express $\log _ { a } x ^ { 4 } + \log _ { a } \left( \frac { 1 } { x } \right)$ as a multiple of $\log _ { a } x$.\\
(ii) Given that $\log _ { 10 } b + \log _ { 10 } c = 3$, find $b$ in terms of $c$.
\hfill \mbox{\textit{OCR MEI C2 2007 Q10 [4]}}