!!!! П О М О Г И Т Е !!!!! Необходимо решить неравенства: а) log2(1 + log1/9(x) –...

А
x>0
1+log(1/9)x+log(1/9)x<2 2log(1/9)x<1 log(1/9)x<1/2 x>1/3
x∈(1/3;∞)
б
x>1
4log²(2)(x-1)+log(2)(x-1)-5>0
log(2)(x-1)=a
4a²+a-5>0
D=1+80=81
a1=(-1-9)/8=-5/4
a2=(-1+9)/8=2
a<-5/4 U a>2
log(2)(x-1)<-5/4⇒x-1<<img src="https://tex.z-dn.net/?f=1%2F2++%5Csqrt%5B4%5D%7B2%7D+" id="TexFormula1" title="1/2 \sqrt[4]{2} " alt="1/2 \sqrt[4]{2} " align="absmiddle" class="latex-formula">⇒x<1+<img src="https://tex.z-dn.net/?f=1%2F2+%5Csqrt%5B4%5D%7B2%7D+" id="TexFormula2" title="1/2 \sqrt[4]{2} " alt="1/2 \sqrt[4]{2} " align="absmiddle" class="latex-formula">
log(2)(x-1)>2⇒x-1>4⇒x>5
x∈(1;1+ $1/2 \sqrt[4]{2}$ ) U (5;∞)
в
ОДЗ
x-1>0⇒x>1
x-1≠1⇒x≠2
x∈(1;2) U (2;∞)
log(2)log(x-1)9<1 log(x-1)9<2 1)x∈(1;2) основание меньше 1,знак меняется
9>(x-1)²
(x-1)²-9<0 (x-1-3)(x-1+3)<0 (x-4)(x+2)<0 x=4 x=-2
-2x∈(1;2)
2)x∈(2;∞)
x<-2 U x>4
x∈(4;∞)
общий x∈(1;2) U (4;∞)
г
x>0
log(1/3)log(5)x>1
log(5)x<1/3 x<∛5 x∈(0;∛5)