- Find the equation of the normal to the curve \(y = 4 \ln ( 2 x - 3 )\) at the point where the curve crosses the \(x\) axis. Give your answer in the form \(a x + b y + k = 0\) where \(a > 0\).
i) Write \(\log _ { 16 } y - \log _ { 16 } x\) as a single logarithm.
ii) Solve the simultaneous equations, giving your answers in an exact form.
$$\begin{gathered}
\log _ { 3 } y = \log _ { 3 } ( 9 - 6 x ) + 1
\log _ { 16 } y - \log _ { 16 } x = \frac { 1 } { 4 }
\end{gathered}$$