5. (i) Anna, who is confused about the rules for logarithms, states that $$\left( \log _ { 3 } p \right) ^ { 2 } = \log _ { 3 } \left( p ^ { 2 } \right)$$ and \(\quad \log _ { 3 } ( p + q ) = \log _ { 3 } p + \log _ { 3 } q\).
However, there is a value for \(p\) and a value for \(q\) for which both statements are correct.
Find the value of \(p\) and the value of \(q\).
(ii) Solve $$\frac { \log _ { 3 } \left( 3 x ^ { 3 } - 23 x ^ { 2 } + 40 x \right) } { \log _ { 3 } 9 } = 0.5 + \log _ { 3 } ( 3 x - 8 ) .$$