7. A student was asked to solve the equation \(2 \left( \log _ { 3 } x \right) ^ { 2 } - 3 \log _ { 3 } x - 2 = 0\). The student's attempt is written out below.
$$\begin{aligned}
& 2 \left( \log _ { 3 } x \right) ^ { 2 } - 3 \log _ { 3 } x - 2 = 0
& 4 \log _ { 3 } x - 3 \log _ { 3 } x - 2 = 0
& \log _ { 3 } x - 2 = 0
& \log _ { 3 } x = 2
& x = 8
\end{aligned}$$
- Identify the two mistakes that the student has made.
- Solve the equation \(2 \left( \log _ { 3 } x \right) ^ { 2 } - 3 \log _ { 3 } x - 2 = 0\), giving your answers in an exact form.
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