16.
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\includegraphics[alt={},max width=\textwidth]{8053bd07-c2b2-4ada-ae0e-8ab6b8466c78-34_606_737_146_760}
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\caption{Figure 6
In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.}
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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 \(\frac { 3 + 2 \log _ { 2 } 3 } { 3 + \log _ { 2 } 3 }\).
[0pt]
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