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October 2021 2 23 Report

1)[tex]( \sqrt{6} )^x \leq \frac{1}{36} [/tex]
2) [tex]0,2 ^x \leq \frac{1}{25} [/tex]
3) [tex](1,5)^x<2,25[/tex]

Хильмилли 1) (6^(1/2))^x<=6^(-2)⇒6^(x/2)<=6^(-2)
Основание равно 6>1; функция возрастающая⇒x/2<=-2⇒x<=-4⇒x∈(-∞;-4]
2) 0,2=1/5=5^(-1); 25=5^2; ⇒5^(-x)<=5^(-2); 5>1⇒-x<=-2⇒x>=2⇒x∈[2;+∞)
3) 1,5=3/2; 2,25=2+1/4=9/4=(3/2)^2⇒(3/2)^x<(3/2)^2; 3/2>1⇒x<2⇒x∈{-∞;2)

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admir17 1) $6^{ \frac{x}{2} } \leq 6^{-2}$
$\frac{x}{2} \leq {-2}$
$x \leq -4$

2) $( \frac{1}{5}) ^{x} \leq ( \frac{1}{5}) ^{2}$
$x \geq 2$

3) $(1.5)^{x}$
$x$

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