Question

Показательные уравнения

Answer 1

Вложение .................................................

Answer 2

$( frac{4}{9})^{x} *( frac{27}{8})^{x-1} leq frac{2}{3}$

$( frac{2}{3})^{2x} *( frac{2}{3})^{(-3)(x-1)} leq frac{2}{3}$

$( frac{2}{3})^{2x-3x+3} leq frac{2}{3}$

$-x+3 geq 1$
$x leq 2$


$(frac{4}{25})^{2x+3.75} geq (sqrt{ frac{2}{5}} )^{- x^{2} }$

$(frac{2}{5})^{4x+7.5} geq (frac{2}{5}} )^{- frac{1}{2} x^{2} }$

${4x+7.5}leq-frac{1}{2} x^{2}$

$frac{1}{2} x^{2}+4x+7.5leq0$

$x^{2}+8x+15leq0$

$(x+5)(x+3)leq 0$
$-5 leq x leq-3$


$frac{25^{2+x} }{125^{5-x} } <625$

$frac{5^{4+2x} }{5^{15-3x} } < 5^{4}$

$5^{4+2x-15+3x}< 5^{4}$

$5^{5x-11}< 5^{4}$

${5x-11}< {4}$
$x<3$