Question

Помогите решить показательные неравенства!!

Answer 1

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

2)
$0.3^{3x-1}\ \textless \ 0.09 \\ 0.3^{3x-1} \ \textless \ 0.3^2 \\ 3x-1\ \textgreater \ 2 \\ 3x\ \textgreater \ 3 \\ x\ \textgreater \ 1 \\ x\in(1;+\infty)$

3)
$1.5^x\ \textgreater \ 2.25 \\ 1.5^x\ \textgreater \ 1.5^2 \\ x\ \textgreater \ 2 \\\\ x\in(2;+\infty)$