| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve ln equation using subtraction law |
| Difficulty | Moderate -0.3 Part (a) is routine algebraic factorization and simplification. Part (b) applies the logarithm quotient law (which directly follows from part a) then solves a linear equation. This is a standard C3 exercise testing basic log laws with straightforward algebra, making it slightly easier than average but not trivial due to the multi-step nature and 6 total marks. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\alph*)]
\item Simplify $\frac{x^2 + 4x + 3}{x^2 + x}$. [2]
\item Find the value of $x$ for which $\log_2 (x^2 + 4x + 3) - \log_2 (x^2 + x) = 4$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q25 [6]}}