| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.8 Part (i) is a direct application of logarithms to solve an exponential equation (take log of both sides), requiring only calculator work. Part (ii) uses the log subtraction rule then solving a linear equation after exponentiating—both are standard textbook exercises with no problem-solving insight needed. This is easier than average A-level content. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use or state \(y\log 3 = \log 12\) or \(\log_3 12\) | M1 | Uses power law for logs; may be implied; trial and error valid if \(3^{2.26}=11.9\ldots\) and \(3^{2.27}=12.1\ldots\) shown |
| \(y = 2.26\) or awrt \(2.26\) | A1 | Just the answer with no incorrect working scores 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Use or state \(\log_2 16 = 4\) or \(2^4 = 16\) | B1 | Connects 16 with '4' correctly; can be scored at any time |
| \(\log_2(x+3) - \log_2(2x+4) = \log_2\frac{(x+3)}{(2x+4)}\) | M1 | Correct use of addition or subtraction law of logs |
| \(\frac{x+3}{(2x+4)} = 16\) | A1 | Correct equation not involving logs |
| \(x = -\dfrac{61}{31}\) | A1 | cso |
## Question 5:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use or state $y\log 3 = \log 12$ or $\log_3 12$ | M1 | Uses power law for logs; may be implied; trial and error valid if $3^{2.26}=11.9\ldots$ **and** $3^{2.27}=12.1\ldots$ shown |
| $y = 2.26$ or awrt $2.26$ | A1 | Just the answer with no incorrect working scores 2 marks |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Use or state $\log_2 16 = 4$ or $2^4 = 16$ | B1 | Connects 16 with '4' correctly; can be scored at any time |
| $\log_2(x+3) - \log_2(2x+4) = \log_2\frac{(x+3)}{(2x+4)}$ | M1 | Correct use of addition or subtraction law of logs |
| $\frac{x+3}{(2x+4)} = 16$ | A1 | Correct equation not involving logs |
| $x = -\dfrac{61}{31}$ | A1 | cso |
---\begin{enumerate}
\item (i) Find, giving your answer to 3 significant figures, the value of $y$ for which
\end{enumerate}
$$3 ^ { y } = 12$$
(ii) Solve, giving an exact answer, the equation
$$\log _ { 2 } ( x + 3 ) - \log _ { 2 } ( 2 x + 4 ) = 4$$
(You should show each step in your working.)\\
\hfill \mbox{\textit{Edexcel C12 2015 Q5 [6]}}