| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | State value of basic log |
| Difficulty | Easy -1.8 This is a very straightforward question testing basic logarithm definitions and laws. Part (i) is trivial recall (log_a(a)=1), part (ii) requires recognizing 1/9=3^(-2), and part (iii) is direct application of log laws with no problem-solving. All three parts are routine exercises well below average A-level difficulty. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| (i) 1 | 1 | |
| (ii) \(-2\) | M1 for \(1/9=3^{-2}\) or \(\log(1) - \log(3^2)\) | 2 |
| (iii) \(6\log x\) | base not reqd; M1 for \(5\log x\) or \(\log(x^y)\) | 2 |
| 5 |
(i) 1 | 1
(ii) $-2$ | M1 for $1/9=3^{-2}$ or $\log(1) - \log(3^2)$ | 2
(iii) $6\log x$ | base not reqd; M1 for $5\log x$ or $\log(x^y)$ | 2
| | 55 (i) Write down the value of $\log _ { 5 } 5$.\\
(ii) Find $\log _ { 3 } \left( \frac { 1 } { 9 } \right)$.\\
(iii) Express $\log _ { a } x + \log _ { a } \left( x ^ { 5 } \right)$ as a multiple of $\log _ { a } x$.
\hfill \mbox{\textit{OCR MEI C2 2005 Q5 [5]}}