0} \atop {(x-2)^2>0\; ,\; |x-2|>0}} \right. \; \Rightarrow \; \; \left \{ {{x<2} \atop {x\ne 2}} \right. \; \Rightarrow \; \; \underline {x<2}\\\\\boxed {\; log_{a}x^2=2\cdot log_{a}|x|\; ,\; a>0\; ,\; a\ne 1}\\\\log_2^2(2-x)-2\cdot log_2|x-2|+3\cdot log_2|x-2|-2=0\\\\Tak\; kak\; x<2,\; to\; (x-2)<0\; \; \Rightarrow \; \; |x-2|=-(x-2)=2-x\; \; \Rightarrow \\\\\Big (log_2(2-x)\Big )^2+log_2(2-x)-2=0\\\\t=log_2(2-x)\; ,\; \; t^2+t-2=0\; ," alt="log_2^2(2-x)-log_2(x-2)^2+3\, log_2|x-2|=2\\\\ODZ:\; \; \left \{ {{2-x>0} \atop {(x-2)^2>0\; ,\; |x-2|>0}} \right. \; \Rightarrow \; \; \left \{ {{x<2} \atop {x\ne 2}} \right. \; \Rightarrow \; \; \underline {x<2}\\\\\boxed {\; log_{a}x^2=2\cdot log_{a}|x|\; ,\; a>0\; ,\; a\ne 1}\\\\log_2^2(2-x)-2\cdot log_2|x-2|+3\cdot log_2|x-2|-2=0\\\\Tak\; kak\; x<2,\; to\; (x-2)<0\; \; \Rightarrow \; \; |x-2|=-(x-2)=2-x\; \; \Rightarrow \\\\\Big (log_2(2-x)\Big )^2+log_2(2-x)-2=0\\\\t=log_2(2-x)\; ,\; \; t^2+t-2=0\; ," align="absmiddle" class="latex-formula">
