| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve by showing reduces to polynomial |
| Difficulty | Standard +0.3 Part (a) is straightforward application of log laws (log of product and power). Part (b) requires substituting the result from (a) and recognizing that log₃y = log₃(28x-9) implies y = 28x-9, leading to a simple quadratic 3x² = 28x - 9. This is a standard multi-step question with clear scaffolding, slightly easier than average due to the helpful hint in part (a). |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
9. Given that $y = 3 x ^ { 2 }$,
\begin{enumerate}[label=(\alph*)]
\item show that $\log _ { 3 } y = 1 + 2 \log _ { 3 } x$
\item Hence, or otherwise, solve the equation
$$1 + 2 \log _ { 3 } x = \log _ { 3 } ( 28 x - 9 )$$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q9 [6]}}