\frac{1}{2}lg3,\; lgx>lg\sqrt3,\; x>\sqrt3\\\\x\in (\sqrt3,+\infty)\\\\2)\; |log_2x| \leq 3\; \to \\\\-3 \leq log_2x \leq 3\; \to \left \{ {{log_2x \leq 3} \atop {log_2x \geq -3}} \right. \; \left \{ {{x \leq 2^3} \atop {x \geq 2^{-3}}} \right.\; \to x\in [\frac{1}{8},8] " alt="log_{x}3=\frac{lg3}{lgx},\; \frac{lg3}{lgx}<2\\\\lgx>\frac{1}{2}lg3,\; lgx>lg\sqrt3,\; x>\sqrt3\\\\x\in (\sqrt3,+\infty)\\\\2)\; |log_2x| \leq 3\; \to \\\\-3 \leq log_2x \leq 3\; \to \left \{ {{log_2x \leq 3} \atop {log_2x \geq -3}} \right. \; \left \{ {{x \leq 2^3} \atop {x \geq 2^{-3}}} \right.\; \to x\in [\frac{1}{8},8] " align="absmiddle" class="latex-formula">