Задача 73605 ...
Условие
2. log(0,3)(-x+2) ≤ log(0,3)(2x-2)
....
Решение
2.
[m]\left\{\begin {matrix}-x+2>0\\2x-2>0\\-x+2 ≥ 2x-2 ⇒-3x ≥ -4 , \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x<2\\ x>1\\x ≤ 1\frac{1}{3}\end {matrix}\right.[/m]
О т в е т. (1;[m] 1\frac{1}{3}][/m]
3.
[m]\left\{\begin {matrix}4x+12>0\\4x+12≤10 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>-3\\ x ≤-\frac{2}{3}\end {matrix}\right.[/m]
О т в е т. (-3;[m] -\frac{2}{3}][/m]
4.
[m]\left\{\begin {matrix}1+x>0\\-x>0\\1+x>-x⇒2x>-1 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>-1\\ x <0\\x>-\frac{1}{2}\end {matrix}\right.[/m]
О т в е т. ([m] -\frac{1}{2};0)[/m]
5.
[m]log_{0,5}(8x+5) ≥ -2[/m]
[m]log_{0,5}(8x+5) ≥ -2log_{0,5}0,5[/m]
[m]log_{0,5}(8x+5) ≥ log_{0,5}0,5^{-2}[/m]
[m]log_{0,5}(8x+5) ≥ log_{0,5}4[/m]
[m]\left\{\begin {matrix}8x+5>0\\8x+5≤4 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>-\frac{5}{8}\\ x ≤-\frac{1}{8}\end {matrix}\right.[/m]
О т в е т. ([m]-\frac{5}{8}; -\frac{1}{8}][/m]
6.
[m]3 ≥ log_{5}x^3[/m]
[m]log_{5}5^3 ≥ log_{5}x^3[/m]
[m]\left\{\begin {matrix}x^3>0\\x^3≤5^3 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>0\\ x ≤5\end {matrix}\right.[/m]
О т в е т. ([m]0;5][/m]
7.
[m]log_{2}(x^2-7x+18) ≤3[/m]
[m]log_{2}(x^2-7x+18) ≤3log_{2}2[/m]
[m]log_{2}(x^2-7x+18) ≤log_{2}2^3[/m]
[m]\left\{\begin {matrix}x^2-7x+18>0\\x^2-7x+18≤8 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}D=(-7)^2-4\cdot 18<0, неравенство. верно. при. любых. х\\x^2-7x+10≤0; D=9 ⇒ x ∈ [2;5]\end {matrix}\right.[/m]
О т в е т. [2;5]
8.
[m]lg\sqrt{x-1}<-1[/m]
[m]lg\sqrt{x-1}<lg0,1[/m]
[m]\left\{\begin {matrix}x-1>0\\\sqrt{x-1}<0,1 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>1\\(\sqrt{x-1})^2<0,1^2 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>1\\x-1<0,1^2 \end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>1\\x<1,01 \end {matrix}\right.[/m]
О т в е т. (1; 1,01)
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1.
[m]\left\{\begin {matrix}x+4>0\\x^2+2x-2>0\\x+4 < x^2+2x-2, логарифмическая.функция. с. основанием.0<0,3<1.убывающая\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x>-4\\D=12; x < -1-\sqrt{3}; x>-1+\sqrt{3}\\ x^2+x-6>0, D=25, x<-3; x>2\end {matrix}\right.[/m]
О т в е т. (-4:-3) U (2;+ ∞ )
