| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.8 Part (a) is a direct application of logarithms to solve an exponential equation (take log of both sides), and part (b) uses basic logarithm laws (difference of logs becomes quotient) followed by simple algebraic manipulation. Both are routine C2 exercises requiring only standard techniques with no problem-solving insight needed. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(x\log 5 = \log 8\), \(x = \frac{\log 8}{\log 5} = 1.29\) | M1, A1, A1 | Answer only 1.29: full marks; rounds to 1.29 (e.g. 1.292): M1 A1 A0; rounds to 1.3: M1 A0 A0. Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\log_2 \frac{x+1}{x}\) (or \(\log_2 7x\)) | B1 | |
| \(\frac{x+1}{x} = 7\), \(x = \frac{1}{6}\) (Allow 0.167 or better) | M1, A1 | M1: form and solve equation in \(x\) by legitimate log work; answer only: no marks unless verified. Total: 3 |
## Question 2:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $x\log 5 = \log 8$, $x = \frac{\log 8}{\log 5} = 1.29$ | M1, A1, A1 | Answer only 1.29: full marks; rounds to 1.29 (e.g. 1.292): M1 A1 A0; rounds to 1.3: M1 A0 A0. **Total: 3** |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\log_2 \frac{x+1}{x}$ (or $\log_2 7x$) | B1 | |
| $\frac{x+1}{x} = 7$, $x = \frac{1}{6}$ (Allow 0.167 or better) | M1, A1 | M1: form and solve equation in $x$ by legitimate log work; answer only: no marks unless verified. **Total: 3** |
---Solve
\begin{enumerate}[label=(\alph*)]
\item $5 ^ { x } = 8$, giving your answer to 3 significant figures,
\item $\log _ { 2 } ( x + 1 ) - \log _ { 2 } x = \log _ { 2 } 7$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2005 Q2 [6]}}