0,} \atop {x>0;}} \right. \ \left \{ {{x>2,} \atop {x>0;}} \right. \ x>2; \\ x\in(2;\+\infty), \\ log_2(x-2)+log_2x\leq3, \\ log_2(x(x-2))\leq3, \\ 2>1, \\ x^2-2x\leq2^3, \\ x^2-2x-8\leq0, \\ x^2-2x-8=0, \\ x_1=-2, x_2=4, \\ (x+2)(x-4)\leq0, \\ -2\leq x\leq4, \\ x\in(2;4]." alt="log_2(x-2)\leq3-log_2x, \\ \left \{ {{x-2>0,} \atop {x>0;}} \right. \ \left \{ {{x>2,} \atop {x>0;}} \right. \ x>2; \\ x\in(2;\+\infty), \\ log_2(x-2)+log_2x\leq3, \\ log_2(x(x-2))\leq3, \\ 2>1, \\ x^2-2x\leq2^3, \\ x^2-2x-8\leq0, \\ x^2-2x-8=0, \\ x_1=-2, x_2=4, \\ (x+2)(x-4)\leq0, \\ -2\leq x\leq4, \\ x\in(2;4]." align="absmiddle" class="latex-formula">