12.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-11_572_675_1098_772}
\captionsetup{labelformat=empty}
\caption{Figure 6}
\end{figure}
\section*{In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.}
Figure 6 shows a sketch of part of the curve with equation
$$y = 3 \times 2 ^ { 2 x }$$
The point \(P ( a , 96 \sqrt { 2 } )\) lies on the curve.
- Find the exact value of \(a\).
The curve with equation \(y = 3 \times 2 ^ { 2 x }\) meets the curve with equation \(y = 6 ^ { 3 - x }\) at the point \(Q\).
- Show that the \(x\) coordinate of \(Q\) is
$$\frac { 3 + 2 \log _ { 2 } 3 } { 3 + \log _ { 2 } 3 }$$