Solve the system of inequalities $$\left\{ \begin{array} { l }
\log _ { 3 } | x - 3 | < 4 \\
\log _ { 2 } x + \log _ { 2 } ( x - 2 ) \geqq 3
\end{array} \right.$$ and find the number of integers $x$ that satisfy it. [3 points]
Solve the system of inequalities
$$\left\{ \begin{array} { l }
\log _ { 3 } | x - 3 | < 4 \\
\log _ { 2 } x + \log _ { 2 } ( x - 2 ) \geqq 3
\end{array} \right.$$
and find the number of integers $x$ that satisfy it. [3 points]