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