[tex]\log_x3<1\\\\D:x\not =1 \wedge x>0\\D:x\in(0,1)\cup(1,\infty)\\\\\log_x3<1\\\log_x3<\log_xx\\\\\underline{1.\ x\in(0,1)}\\3>x\\x\in(-\infty,3)\\\\x\in(-\infty,3) \wedge x\in(0,1)\\x\in(0,1)\\\\\underline{2.\ x\in(1,\infty)}\\3<x\\x\in(3,\infty)\\\\x\in(3,\infty) \wedge x\in(1,\infty)\\x\in(3,\infty)\\\\x\in(0,1)\vee x\in(3,\infty)\\\boxed{x\in(0,1)\cup(3,\infty)}[/tex]
