1) 7^(1/3)*7^(-2/3)*7^(4/3)=7
2) log [8] log [4] log [2] 16= log [8] log [4] 4 =log [8] 1 = 0
3) sqrt(x-5)+sqrt(10-x)=3
одз x>=5 x<=10</p>
x-5+10-x +2 sqrt((x-5)(10-x))=9
sqrt((x-5)(10-x))=2
(x-5)(10-x)=4
10x-50-x^2+5x=4
x^2-15x+54=0
D=225-4*54=225-216=9
x=6
x=9
4) 3^(x+2) + 4*3^(x+1)=21
3y+4y=21
y=7
3^(x+1)=3
x=0
5) 2/(lg x-1)+ 4/(lg x +3)=1
2/(y-1) +4/(y+3)=1
2y+6+4y-4=y^2-y+3y-3
6y+2=y^2+2y-3
y^2-4y-5=0
y=5 y=-1
lg x=5
x=10^5
lg x=-1
x=0.1
6) (1/3)^(3x^2+3)>=(1/3)^(-2x^2+16x)
3x^2+3<=-2x^2+16x</p>
5x^2-16x+3<=0</p>
D=256-60=196=14^2
x<=3</p>
x>=0.2
7)
(log[0.5]x)^2+3(log[0.5]x)<0</p>
y^2+3y<0</p>
y>-3 y<0</p>
log[0.5]x <0</p>
x<1</p>
log[0.5]x>-3
x>0.125
0.125