Question

Решите неравенство:
1. $5^{-x}>625$
2. $( frac{4}{3}) ^{2x-1} geq frac{3}{4}$
3. $( frac{1}{3}) ^{5 x^{2} +8x-4} leq 1$
4. $5^{2x}-6* 5^{x}+5>0$
5. $sqrt{ 6^{x} } geq 216$

Answer 1

$1. 5^{-x}>625, \ 5^{-x}>5^4, \ 5>1, -x>4, \ x<-4;$
$2. (frac{4}{3}) ^{2x-1} geq frac{3}{4}, \ (frac{4}{3}) ^{2x-1} geq (frac{4}{3})^{-1}, \ frac{4}{3}>1, 2x-1 geq -1, \ 2x geq 0, \ x geq 0;$
$3. (frac{1}{3}) ^{5 x^{2} +8x-4} leq 1, \ (frac{1}{3}) ^{5 x^{2} +8x-4} leq (frac{1}{3}) ^{0}, \ frac{1}{3}<1, 5 x^{2} +8x-4 geq 0, \ 5 x^{2} +8x-4=0, \ D_{/4}=36, \ x_1=-2, x_2= frac{2}{5}, \ left [ {{x leq -2,} atop {x geq 0,4;}} right.$
$5. 5^{2x}-6cdot5^{x}+5>0 , \ 5^{x}=a, a^2-6a+5>0, \ a^2-6a+5=0, \ a_1=1, a_2=5, \ left [ {{a<1,} atop {a>5;}} right. left [ {{5^{x}<1,} atop {5^{x}>5;}} right. left [ {{x<0,} atop {x>1;}} right.$
$6. sqrt{6^{x}} geq 216, \ 6^{frac{x}{2}} geq 6^3, \ frac{x}{2} geq 3, \ x geq 6.$