| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2016 |
| Session | October |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.8 This is a straightforward two-part question testing basic logarithm manipulation and recall of definitions. Part (a) requires taking logs of both sides and dividing, while part (b) requires converting the logarithm to exponential form. Both are routine textbook exercises with no problem-solving or insight required, making this easier than average. |
| Spec | 1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2x\log 7 = \log 14\) or \(x\log 49 = \log 14\) or \(2x = \log_7 14\) | M1 | Uses logs and brings down \(x\) correctly |
| \(x = \frac{\log 14}{2\log 7}\) | M1 | Makes \(x\) subject correctly; must follow method involving taking logs |
| \(= \text{awrt } 0.678\) | A1 | Accept awrt 0.678 (correct answer with no working implies two previous marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(3x + 1 = 5^{-2}\) | M1 | Uses powers correctly to undo log; accept \(3x+1=0.04\) |
| \(x = -\frac{8}{25}\) or \(-0.32\) | A1 | Correct answer implies method mark; accept \(-0.320\) |
## Question 2:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2x\log 7 = \log 14$ or $x\log 49 = \log 14$ or $2x = \log_7 14$ | M1 | Uses logs and brings down $x$ correctly |
| $x = \frac{\log 14}{2\log 7}$ | M1 | Makes $x$ subject correctly; must follow method involving taking logs |
| $= \text{awrt } 0.678$ | A1 | Accept awrt 0.678 (correct answer with no working implies two previous marks) |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $3x + 1 = 5^{-2}$ | M1 | Uses powers correctly to undo log; accept $3x+1=0.04$ |
| $x = -\frac{8}{25}$ or $-0.32$ | A1 | Correct answer implies method mark; accept $-0.320$ |
---2. Find, giving your answer to 3 significant figures where appropriate, the value of $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $7 ^ { 2 x } = 14$
\item $\log _ { 5 } ( 3 x + 1 ) = - 2$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2016 Q2 [5]}}