5. (a) Given that \(3 + 2 \log _ { 2 } x = \log _ { 2 } y\), show that \(y = 8 x ^ { 2 }\).
(b) Hence, or otherwise, find the roots \(\alpha\) and \(\beta\), where \(\alpha < \beta\), of the equation $$3 + 2 \log _ { 2 } x = \log _ { 2 } ( 14 x - 3 )$$ (c) Show that \(\log _ { 2 } \alpha = - 2\).
(d) Calculate \(\log _ { 2 } \beta\), giving your answer to 3 significant figures.