| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Express log in terms of given variables |
| Difficulty | Moderate -0.8 This is a straightforward application of logarithm laws (product, quotient, and power rules) with no problem-solving required. Students need to express 45 as 3²×5 and 0.3 as 3/10, then apply log rules mechanically. It's easier than average as it's pure recall and manipulation, though slightly more involved than single-step index law questions. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(= \log_2(3^2 \times 5)\) | B1 | |
| \(= 2\log_2 3 + \log_2 5 = 2p + q\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(= \log_2 \frac{3}{5 \times 2} = \log_2 3 - \log_2 5 - \log_2 2\) | M1 | |
| \(= p - q - 1\) | B1 A1 | (6) |
## Question 3:
**(a)**
| Answer/Working | Marks | Notes |
|---|---|---|
| $= \log_2(3^2 \times 5)$ | B1 | |
| $= 2\log_2 3 + \log_2 5 = 2p + q$ | M1 A1 | |
**(b)**
| Answer/Working | Marks | Notes |
|---|---|---|
| $= \log_2 \frac{3}{5 \times 2} = \log_2 3 - \log_2 5 - \log_2 2$ | M1 | |
| $= p - q - 1$ | B1 A1 | **(6)** |
---3. Given that $p = \log _ { 2 } 3$ and $q = \log _ { 2 } 5$, find expressions in terms of $p$ and $q$ for
\begin{enumerate}[label=(\alph*)]
\item $\quad \log _ { 2 } 45$,
\item $\quad \log _ { 2 } 0.3$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [6]}}