0\; ,\; \; \; +++(1)---(2)+++\\\\x\in (-\infty ,1)\cup(2,+\infty )\\\\log_4\, \frac{x-1}{2x-4}\leq log_4\, 1\\\\\frac{x-1}{2x-4}\leq 1\; ,\; \; \frac{x-1-2x+4}{2x-4}\leq 0\; ,\; \; \frac{-x+3}{2x-4}\leq 0\; ,\; \; \frac{x-3}{2x-4}\geq 0\; ,\\\\+++(2)---(3)+++\\\\x\in (-\infty ,2)\cup [\, 3,+\infty )\\\\\left \{ {{x\in (-\infty ,1)\cup (2,+\infty )} \atop {x\in (-\infty ,2)\cup [\, 3,+\infty )}} \right. \; \; \Rightarrow \; \; \; x\in (-\infty , 1)\cup [\, 3,+\infty )" alt=" log_4\, \frac{x-1}{2x-4}\leq 0\; ,\\\\ODZ:\; \frac{x-1}{2x-4}>0\; ,\; \; \; +++(1)---(2)+++\\\\x\in (-\infty ,1)\cup(2,+\infty )\\\\log_4\, \frac{x-1}{2x-4}\leq log_4\, 1\\\\\frac{x-1}{2x-4}\leq 1\; ,\; \; \frac{x-1-2x+4}{2x-4}\leq 0\; ,\; \; \frac{-x+3}{2x-4}\leq 0\; ,\; \; \frac{x-3}{2x-4}\geq 0\; ,\\\\+++(2)---(3)+++\\\\x\in (-\infty ,2)\cup [\, 3,+\infty )\\\\\left \{ {{x\in (-\infty ,1)\cup (2,+\infty )} \atop {x\in (-\infty ,2)\cup [\, 3,+\infty )}} \right. \; \; \Rightarrow \; \; \; x\in (-\infty , 1)\cup [\, 3,+\infty )" align="absmiddle" class="latex-formula">