Question

Показательные уравнения и неравенства.

Answer 1

$1)(\frac{1}{8})^{-3+x}\leq 512\\2^{-3x+9}\leq 2^9\\9-3x\leq 9\\-3x\leq 0\\x\geq 0\\2)(\frac{1}{9} )^{x-13}\geq 3\\3^{26-2x}\geq 3\\26-2x\geq 1\\-2x\geq -25\\x\leq 12,5\\3)(\frac{1}{2} )^{10-3x}\leq 32\\2^{3x-10}\leq 2^5\\3x\leq 15\\x\leq 5$

Answer 2

$1)(\frac{1}{8})^{-3+x}\leq512\\\\((2^{-3}))^{-3+x}\leq2^{9}\\\\2^{-3x+9}\leq2^{9} \\\\2>1\Rightarrow -3x+9\leq9\\\\-3x\leq 0\\\\x\geq 0\\\\Otvet:\boxed{ x\in[0;+\infty)}$

$2)(\frac{1}{9})^{x-13}\geq 3\\\\((3^{-2}))^{x-13}\geq3\\\\3^{-2x+26}\geq3\\\\3>1\Rightarrow -2x+26\geq1\\\\-2x\geq-25\\\\x\leq12,5\\\\Otvet:\boxed {x\in(-\infty;12,5]}$

$3)(\frac{1}{2})^{10-3x}\leq32\\\\((2^{-1}))^{10-3x}\leq2^{5}\\\\2^{3x-10}\leq2^{5}\\\\2>1\Rightarrow 3x-10\leq5\\\\3x\leq15\\\\x\leq 5\\\\Otvet:\boxed {x\in(-\infty;5]}$