| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Evaluate log expression using laws |
| Difficulty | Easy -1.3 This is a straightforward application of basic logarithm laws (power rule and subtraction rule) with no problem-solving required. Both parts are direct one-step simplifications using standard rules that students practice routinely, making it easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| (i) \(17\log_{10}x\) or \(\log_{10}x^{17}\) | B2 | M1 for \(5\log_{10}x\) or \(12\log_{10}x\) or \(\log_{10}x^{12}\) as part of the first step |
| (ii) \(-b\) | B2 | M1 for \(\log_a 1 = 0\) or \(\log_a a = 1\) soi |
**Question 7:**
| Answer | Mark | Guidance |
|--------|------|----------|
| (i) $17\log_{10}x$ or $\log_{10}x^{17}$ | **B2** | **M1** for $5\log_{10}x$ or $12\log_{10}x$ or $\log_{10}x^{12}$ as part of the first step | condone omission of base |
| (ii) $-b$ | **B2** | **M1** for $\log_a 1 = 0$ or $\log_a a = 1$ soi | allow $0-b$ |
---7 Simplify\\
(i) $\log _ { 10 } x ^ { 5 } + 3 \log _ { 10 } x ^ { 4 }$,\\
(ii) $\log _ { a } 1 - \log _ { a } a ^ { b }$.
\hfill \mbox{\textit{OCR MEI C2 2011 Q7 [4]}}