| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: both solve equations |
| Difficulty | Standard +0.3 Part (a) is trivial manipulation of logarithms (1 mark). Part (b) requires recognizing the substitution u = ln x to form a quadratic, solving it, then exponentiating—a standard technique for C3 but requires multiple steps and careful algebraic manipulation across 5 marks. Overall slightly above average difficulty due to the substitution insight needed, but still a routine exam question. |
| Spec | 1.06d Natural logarithm: ln(x) function and properties1.06f Laws of logarithms: addition, subtraction, power rules |
\begin{enumerate}[label=(\alph*)]
\item Given that $3\ln x = 4$, find the exact value of $x$. [1]
\item By forming a quadratic equation in $\ln x$, solve $3\ln x + \frac{20}{\ln x} = 19$, giving your answers for $x$ in an exact form. [5]
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2011 Q6 [6]}}