1)lg(13x-x^2)>2 lg 2+2 lg 3 2)log9(x^2-6x+8)⩽0,5
Во втором: какой знак перед 0,5?
<=
1) lg (13x - x²) > 2 lg 2 + 2 lg 3 lg (13x - x²) > lg 4 + lg 9 lg (13x - x²) > lg 36 13x - x² > 36 x² - 13x + 36 < 0 (x - 4)(x - 9) < 0 x ∈ (4; 9) 2) log₉(x² - 6x + 8) ≤ 0,5 0 < x² - 6x + 8 ≤ 3 x ∈ [1 ; 2) ∪ (4 ; 5]
![\left \{ {{x^2-6x+8 \ \textgreater \ 0} \atop {x^2-6x+5 \leq 0}} \right. \\ \\ \left \{ {{(x-2)(x-4)\ \textgreater \ 0} \atop {(x-1)(x-5)\leq 0}} \right. \\ \\\left \{ {{xE(-oo; 2)U(4;+oo)} \atop {xE[1;5]}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%5E2-6x%2B8+%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Bx%5E2-6x%2B5++%5Cleq+0%7D%7D+%5Cright.++%5C%5C++%5C%5C+%5Cleft+%5C%7B+%7B%7B%28x-2%29%28x-4%29%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B%28x-1%29%28x-5%29%5Cleq+0%7D%7D+%5Cright.+%5C%5C++%5C%5C%5Cleft+%5C%7B+%7B%7BxE%28-oo%3B+2%29U%284%3B%2Boo%29%7D+%5Catop+%7BxE%5B1%3B5%5D%7D%7D+%5Cright. "\left \{ {{x^2-6x+8 \ \textgreater \ 0} \atop {x^2-6x+5 \leq 0}} \right. \\ \\ \left \{ {{(x-2)(x-4)\ \textgreater \ 0} \atop {(x-1)(x-5)\leq 0}} \right. \\ \\\left \{ {{xE(-oo; 2)U(4;+oo)} \atop {xE[1;5]}} \right.")