The curve with equation \(y = 2 \ln ( 8 - x )\) meets the line \(y = x\) at a single point, \(x = \alpha\).
- Show that \(3 < \alpha < 4\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b5f50f17-9f1b-4b4c-baf3-e50de5f2ea9c-08_666_1061_445_502}
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\caption{Figure 2}
\end{figure}
Figure 2 shows the graph of \(y = 2 \ln ( 8 - x )\) and the graph of \(y = x\).
A student uses the iteration formula
$$x _ { n + 1 } = 2 \ln \left( 8 - x _ { n } \right) , \quad n \in \mathbb { N }$$
in an attempt to find an approximation for \(\alpha\).
Using the graph and starting with \(x _ { 1 } = 4\)