Question

показательные логаримические уравнения ​

Answer 1

$1)0,2^{x-4}<0,008\\\\0,2^{x-4}<0,2^{3}\\\\0<0,2<1\Rightarrow x-4>3\\\\x>7\\\\Otvet:\boxed{x\in(7;+\infty)}$

$2)log_{0,5}x>-1\\\\0<0,5<1\Rightarrow\\\\\left \{ {{x<0,5^{-1} } \atop {x>0}} \right.\\\\\left \{ {{x<2} \atop {x>0}} \right. \\\\Otvet:\boxed{x\in(0;2)}$

$3)27^{-\frac{x}{2}}\leq\sqrt{3}\\\\(3^{3})^{-\frac{x}{2}}\leq 3^{\frac{1}{2}}\\\\3^{-\frac{3x}{2}}\leq3^{\frac{1}{2}}\\\\-\frac{3x}{2}\leq\frac{1}{2}\\\\-3x\leq1\\\\x\geq-\frac{1}{3}\\\\Otvet:\boxed{x\in[-\frac{1}{3};+\infty)}$