6. The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots , u _ { n }\) is defined by the recurrence relation $$u _ { n + 1 } = p u _ { n } + 5 , u _ { 1 } = 2 , \text { where } p \text { is a constant. }$$ Given that \(u _ { 3 } = 8\),

1. show that one possible value of \(p\) is \(\frac { 1 } { 2 }\) and find the other value of \(p\). Using \(p = \frac { 1 } { 2 }\),
2. write down the value of \(\log _ { 2 } p\). Given also that \(\log _ { 2 } q = t\),
3. express \(\log _ { 2 } \left( \frac { p ^ { 3 } } { \sqrt { q } } \right)\) in terms of \(t\).
   [0pt] [P2 November 2002 Question 4]