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

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

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