| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Natural logarithm equation solving |
| Difficulty | Standard +0.3 Part (a) is trivial logarithm manipulation (one step). Part (b) requires recognizing a disguised quadratic in ln(x), which is a standard C3 technique, but involves multiple steps including substitution, solving the quadratic, and exponentiating. This is slightly above average difficulty for C3 but remains a textbook exercise type. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules |
5
\begin{enumerate}[label=(\alph*)]
\item Given that $2 \ln x = 5$, find the exact value of $x$.
\item Solve the equation
$$2 \ln x + \frac { 15 } { \ln x } = 11$$
giving your answers as exact values of $x$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2009 Q5 [6]}}