Some algebraic implications of inequalities

Q. Which of the following is/are not the solution of ${\log }_3\left(x^2-2\right)<{\log }_3\left(\frac{3}{2}\left|x\right|-1\right)$

1. $\left(\sqrt{2},2\right)$
2. $\left(-2,-\sqrt{2}\right)$
3. $\left(-\sqrt{2},2\right)$
4. $\left(-2,2\right)$

Q. Let $a={\log }_3{\log }_{3}2.$ An integer k satisfying $1<2^{\left(-k+3^{-a}\right)}<2,$ is