11 In this question you must show detailed reasoning.
- A student is asked to solve the inequality \(x ^ { \frac { 1 } { 2 } } < 4\).
The student argues that \(x ^ { \frac { 1 } { 2 } } < 4 \Leftrightarrow x < 16\), so that the solution is \(\{ x : x < 16 \}\).
Comment on the validity of the student's argument. - Solve the inequality \(\left( \frac { 1 } { 2 } \right) ^ { x } < 4\).
- Show that the equation \(2 \log _ { 2 } ( x + 8 ) - \log _ { 2 } ( x + 6 ) = 3\) has only one root.