[tex]\displaystyle\bf\\log_2\Big(x^2-4x+4\Big)=0\\\\x^2-4x+4=2^0\\\\x^2-2\cdot2\cdot x+2^2=1\\\\\Big(x-2\Big)^2=1\\\\\Big(x-2\Big)^2-1=0\\\\\Big(x-2\Big)^2-1^2=0\\\\\text{Folosim formula: }~~a^2-b^2=(a+b)(a-b)\\\\\Big(x-2\Big)^2-1^2=(x-2+1)(x-2-1)=0\\\\(x-1)(x-3)=0\\\\(x-1)=0\implies~\boxed{\bf~x_1=1}\\\\(x-3)=0\implies~\boxed{\bf~x_2=3}[/tex]
