5. A student is asked to solve the equation $$\log _ { 3 } x - \log _ { 3 } \sqrt { x - 2 } = 1$$ The student's attempt is shown $$\begin{aligned} \log _ { 3 } x - \log _ { 3 } \sqrt { x - 2 } & = 1
x - \sqrt { x - 2 } & = 3 ^ { 1 }
x - 3 & = \sqrt { x - 2 }
( x - 3 ) ^ { 2 } & = x - 2
x ^ { 2 } - 7 x + 11 & = 0
x = \frac { 7 + \sqrt { 5 } } { 2 } \quad \text { or } \quad x & = \frac { 7 - \sqrt { 5 } } { 2 } \end{aligned}$$ a. Identify the error made by this student, giving a brief explanation.
b. Write out the correct solution.