Решение на фото.... .........
X²+3x-24=0 ; x²+3x=24 ; 5x=24 ; x=4,8
-1≤sin3x≤1
-4+(-1)≤-4+sin3x≤-4+1
-5≤-4+sin3x≤-3
y∈[-5,-3]
(log(2)2x^-1/log(2)x * log(2)2x²/log(2)x) : (log(2)x/log(2)2x * log(2)x/log(2)2x^-2)<40
((1-log(2)x)(1+2log(2)x)(1+log(2)x)(1-2log(2)x)-40log(2)^4 x)/log(2)^4 x<0
((1-log²(2)x)(1-4log²(2)x)-40log(2)^4 x)/log(2)^4 x<0
(1-4log²(2)x-log²(2)x+4log(2)^4 x-40log(2)^4 x)/log(2)^4 x<0
(1-5log²(2)x-36log(2)^4 x)/log(2)^4 x<0
1-5log²(2)x-36log(2)^4 x<0, log(2)^4 x>0 при любом х>0
36log(2)^4 x +5log²(2)x-1>0
log²(2)x=a
36a²+5a-1>0
D=25+144=169 √D=13
a1=(-5-13)/72=-1/4
a2=(-5+13)/72=1/9
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-1/4 1/9
a<-1/4⇒og²(2)x<-1/4-нет решения
a>1/9⇒log²(2)x>1/9⇒(log(2)x-1/3)(log(2)x+1/3)>0
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-1/3 1/3
log(2)x<-1/3⇒x<1/∛2 и log(2)x>1/3⇒x>∛2