2. Solve the inequality

$$
\log _{2} \frac{6 x+2}{x-2}>2
$$
Solution. The given inequality is equivalent to the inequality

$$
\frac{6 x+2}{x-2}>4
$$

and that is, equivalent to the inequality

$$
(6 x+2)(x-2)>4(x-2)^{2}
$$

i.e., to

$$
x^{2}+3 x-10>0
$$

from which we obtain that $x \in(-\infty,-5) \cup(2,+\infty)$.