| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.8 This is a straightforward C2 logarithm question testing standard techniques: (a) requires taking logs of both sides and rearranging, (b) uses log laws to combine terms then solve. Both are routine textbook exercises with no problem-solving insight required, making them easier than average, though not trivial since they do require correct application of logarithm rules. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \((x - 2) \lg 3 = \lg 5\) | M1 | |
| \(x = \frac{\lg 5}{\lg 3} + 2 = 3.46\) (3sf) | M1 A1 | |
| (b) \(\log_2 (6 - y) + \log_2 y = 3\) | ||
| \(\log_2 [y(6 - y)] = 3\) | M1 | |
| \(y(6 - y) = 2^3 = 8\) | M1 | |
| \(y^2 - 6y + 8 = 0\) | ||
| \((y - 2)(y - 4) = 0\) | M1 | |
| \(y = 2, 4\) | A1 | (7 marks) |
**(a)** $(x - 2) \lg 3 = \lg 5$ | M1 |
$x = \frac{\lg 5}{\lg 3} + 2 = 3.46$ (3sf) | M1 A1 |
**(b)** $\log_2 (6 - y) + \log_2 y = 3$ | |
$\log_2 [y(6 - y)] = 3$ | M1 |
$y(6 - y) = 2^3 = 8$ | M1 |
$y^2 - 6y + 8 = 0$ | |
$(y - 2)(y - 4) = 0$ | M1 |
$y = 2, 4$ | A1 | (7 marks)4. Solve each equation, giving your answers to an appropriate degree of accuracy.
\begin{enumerate}[label=(\alph*)]
\item $3 ^ { x - 2 } = 5$
\item $\quad \log _ { 2 } ( 6 - y ) = 3 - \log _ { 2 } y$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [7]}}