4
- 1
- 10 \end{array} \right) \text { and } \mathbf { d } = \left( \begin{array} { c } - 4
2
- 11 \end{array} \right)$$ （a）Find the position vector of \(E\) ． The volume of a tetrahedron is given by the formula $$\text { volume } = \frac { 1 } { 3 } ( \text { area of base } ) \times ( \text { height } )$$ （b）Find the volume of the tetrahedron \(A B C D\) ． 4．（a）Given that \(x > 0 , y > 0 , x \neq 1\) and \(n > 0\) ，show that $$\log _ { x } y = \log _ { x ^ { n } } y ^ { n }$$ （b）Solve the following，leaving your answers in the form \(2 ^ { p }\) ，where \(p\) is a rational number．
（i） \(\log _ { 2 } u + \log _ { 4 } u ^ { 2 } + \log _ { 8 } u ^ { 3 } + \log _ { 16 } u ^ { 4 } = 5\)
（ii） \(\log _ { 2 } v + \log _ { 4 } v + \log _ { 8 } v + \log _ { 16 } v = 5\)
（iii） \(\log _ { 4 } w ^ { 2 } + \frac { 3 \log _ { 8 } 64 } { \log _ { 2 } w } = 5\)