Question

Срочнооо, помогите :'(

Answer 1

1)
$( frac{1}{4} )^x geq 2 \ 2^{-2x} geq 2^1 \ -2x geq 1 \x leq -0.5$

2)
$2^{3x} leq frac{1}{8} \ 2^{3x} leq 2^{-3} \ 3x leq -3 \x leq -1$

3)
$2^{x^2-4} geq 1 \ 2^{x^2-4} geq 2^0 \x^2-4 geq 0 \ x^2 geq 4 \ x geq 2 cup x leq -2 \xin(-infty;-2]cup[2;+infty)$

4)
$0.7^{x^2-27} textless 0.7 \ x^2-27 textgreater 1 \ x^2 textgreater 28 \ x textgreater sqrt{28} cup x textless -sqrt{28} \xin(-infty;-sqrt{28})cup(sqrt{28};+infty)$

5)
$5^{2-3x}-1 geq 0 \ 5^{2-3x} geq 1 \ 5^{2-3x} geq 5^0 \2-3x geq 0 \-3x geq -2 \x leq frac{2}{3}$

6)
$3^{x+2}+3^{x-1} textless 28 \ 3^x(9+ frac{1}{3} ) textless 28 \3^x* frac{28}{3} textless 28 \ 3^x textless 3 \ x textless 1$

7)
$2^{x-1}+2^{x+3} textgreater 17 \ 2^x( frac{1}{2} +8) textgreater 17 \ 2^x* frac{17}{2} textgreater 17 \ 2^x textgreater 2 \ x textgreater 1$

8)
$9^x-3^x-6 textgreater 0 \ 3^{2x}-3^x-6 textgreater 0 \ 3^x=t \ t^2-t-6 textgreater 0 \ (t-3)(t+2) textgreater 0 \ t-3 textgreater 0 \ 3^x textgreater 3 \ x textgreater 1$

9) 
$4^x-2^x textless 12 \ 2^{2x}-2^x-12 textless 0 \ 2^x=t \ t^2-t-12 textless 0 \(t-4)(t+3) textless 0 \ t-4 textless 0 \ t textless 4 \ 2^x textless 4 \2^x textless 2^2 \ x textless 2$