6. Given that \(\log _ { 3 } x = a\), find in terms of \(a\),
- \(\log _ { 3 } ( 9 x )\)
- \(\log _ { 3 } \left( \frac { x ^ { 5 } } { 81 } \right)\)
giving each answer in its simplest form. - Solve, for \(x\),
$$\log _ { 3 } ( 9 x ) + \log _ { 3 } \left( \frac { x ^ { 5 } } { 81 } \right) = 3$$
giving your answer to 4 significant figures.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4f4eac7b-8908-480f-bb39-049944203fff-10_775_1605_221_159}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The line with equation \(y = 10\) cuts the curve with equation \(y = x ^ { 2 } + 2 x + 2\) at the points \(A\) and \(B\) as shown in Figure 1. The figure is not drawn to scale.