| Exam Board | Edexcel |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve log equation reducing to quadratic |
| Difficulty | Moderate -0.3 This is a straightforward logarithm equation requiring standard log laws (combining logs, simplifying logâ‚‚(16) = 4) and solving a quadratic. It's slightly easier than average because the steps are routine and the base-2 logarithm simplifies nicely, though students must remember to check validity of solutions. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\log_2 a=b \Rightarrow 2^b=a\) | B1 | Correct use: usually from \(\log_2 8=3\) or \(\log_2 16=4\) seen/applied |
| \(\log_2 16x(x+1)=\log_2 8(x+6)\) | M1 | Applies addition/subtraction laws of logs at least once correctly; condone invisible brackets |
| \(2x^2+x-6=0\) | A1 | Or equivalent 3TQ; terms must be collected; can only be scored from correct working |
| \((2x-3)(x+2)=0\) | dM1 | Attempts to solve 3TQ via any valid method; dependent on previous M mark |
| \(x=\frac{3}{2}\) only | A1cso | \(-2\) must be rejected if found; only scored if correct quadratic achieved from correct log work |
# Question 5:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\log_2 a=b \Rightarrow 2^b=a$ | B1 | Correct use: usually from $\log_2 8=3$ or $\log_2 16=4$ seen/applied |
| $\log_2 16x(x+1)=\log_2 8(x+6)$ | M1 | Applies addition/subtraction laws of logs at least once correctly; condone invisible brackets |
| $2x^2+x-6=0$ | A1 | Or equivalent 3TQ; terms must be collected; can only be scored from correct working |
| $(2x-3)(x+2)=0$ | dM1 | Attempts to solve 3TQ via any valid method; dependent on previous M mark |
| $x=\frac{3}{2}$ only | A1cso | $-2$ must be rejected if found; only scored if correct quadratic achieved from correct log work |
---\begin{enumerate}
\item Use the laws of logarithms to solve
\end{enumerate}
$$\log _ { 2 } ( 16 x ) + \log _ { 2 } ( x + 1 ) = 3 + \log _ { 2 } ( x + 6 )$$
\hfill \mbox{\textit{Edexcel P2 2023 Q5 [5]}}