!!!! П О М О Г И Т Е !!!!! Необходимо решить неравенства: а) log2(1 + log1/9(x) – log9(x))<1<br> б) log2^2 (x-1)^2 - log 0.5(x-1)>5 в) log1/2(log2(logx-1 (9)))>0 г) log2(log1/3(log(5x)))>0
А x>0 1+log(1/9)x+log(1/9)x<2<br>2log(1/9)x<1<br>log(1/9)x<1/2<br>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+) 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<br>log(x-1)9<2<br>1)x∈(1;2) основание меньше 1,знак меняется 9>(x-1)² (x-1)²-9<0<br>(x-1-3)(x-1+3)<0<br>(x-4)(x+2)<0<br>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<br>x<∛5<br>x∈(0;∛5)
