(2) Does there exist a real number $k$, such that the inequality $\log _{4}\left(\sqrt{x^{2}+k x+3}-1\right)+$ $\log _{3}\left(x^{2}+k x+2\right) \leqslant 1$ holds for any $x \in[1,2]$? Explain your reasoning.
(2) $-2 \sqrt{2}<k \leqslant-\frac{3}{2}$