12. A student was asked to give the exact solution to the equation
$$2 ^ { 2 x + 4 } - 9 \left( 2 ^ { x } \right) = 0$$
The student's attempt is shown below:
$$\begin{aligned}
& 2 ^ { 2 x + 4 } - 9 \left( 2 ^ { x } \right) = 0
& 2 ^ { 2 x } + 2 ^ { 4 } - 9 \left( 2 ^ { x } \right) = 0
& \text { Let } \quad 2 ^ { x } = y
& y ^ { 2 } - 9 y + 8 = 0
& ( y - 8 ) ( y - 1 ) = 0
& y = 8 \text { or } y = 1
& \text { So } x = 3 \text { or } x = 0
\end{aligned}$$
- Identify the two errors made by the student.
- Find the exact solution to the equation.