log₂(x-2)≤3-log₂x
log₂(x-2)≤log₂8-log₂x
log₂(x-2)≤log₂(8/x)
x-2≤8/x
((x-4)(x+2))/x≤0
(-∞;-2]∨(0;4]
ОДЗ
х>0, х>2
ответ:(2;4]
![log_2(x-2)\leq3-log_2x, \\ \left \{ {{x-20,} \atop {x0;}} \right. \ \left \{ {{x2,} \atop {x0;}} \right. \ x2; \\ x\in(2;\+\infty), \\ log_2(x-2)+log_2x\leq3, \\ log_2(x(x-2))\leq3, \\ 21, \\ 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].](/tpl/images/0172/5057/0449f.png)
