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[latex]log_{(x-1)^2}, (x^2-4x+4) extless 0\\log_{(x-1)^2}, (x-2)^2 extless 0\\ODZ:; ; left{egin{array}{c}(x-2)^2 extgreater 0\(x-1)^2 extgreater 0\(x-1)^2e 1end{array}ight ; left{egin{array}{c}xe 2\xe 1\xe 0; ,; xe 2end{array}ight ; o ; ; xe 0,; xe 1,; xe 2\\((x-1)^2-1)(x^2-4x+4-1) extless 0\\(x^2-2x)(x^2-4x+3) extless 0\\x(x-2)(x-1)(x-3) extless 0\\+++(0)---(1)+++(2)---(3)+++\\xin (0,1)cup (2,3)[/latex]