| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Combine logs into single logarithm |
| Difficulty | Easy -1.2 This is a straightforward application of basic logarithm laws requiring only recall and simple manipulation. Part (i) is trivial recognition that 6²=36, and part (ii) is a standard textbook exercise applying the power and addition laws of logarithms with no problem-solving element. |
| 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) \(2\) | B1 | (1 mark) |
| (ii) \(2\log 3 = \log 3^2\) (or \(2\log p = \log p^2\)) | B1 | |
| \(\log_n p + \log_n 11 = \log_n 11p\) | M1, A1 | Allow e.g. \(\log_n(3^2 \times 11)\) |
| \(= \log_n 99\) | ||
| (4 marks) | Ignore 'missing base' or wrong base. The correct answer with no working scores full marks. \(\log_n 9 \times \log_n 11 = \log_n 99\) or similar mistakes, score M0 A0. |
**(i)** $2$ | B1 | (1 mark) |
| --- | --- | --- |
| **(ii)** $2\log 3 = \log 3^2$ (or $2\log p = \log p^2$) | B1 | |
| $\log_n p + \log_n 11 = \log_n 11p$ | M1, A1 | Allow e.g. $\log_n(3^2 \times 11)$ |
| $= \log_n 99$ | | |
| | (4 marks) | Ignore 'missing base' or wrong base. The correct answer with no working scores full marks. $\log_n 9 \times \log_n 11 = \log_n 99$ or similar mistakes, score M0 A0. |(i) Write down the value of $\log _ { 6 } 36$.\\
(ii) Express $2 \log _ { a } 3 + \log _ { a } 11$ as a single logarithm to base $a$.\\
\hfill \mbox{\textit{Edexcel C2 2006 Q3 [4]}}