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

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

5x^2-16x+3<=0

D=256-60=196=14^2

x<=3

x>=0.2

7)

(log[0.5]x)^2+3(log[0.5]x)<0

y^2+3y<0

y>-3 y<0

log[0.5]x <0

x<1

log[0.5]x>-3

x>0.125

0.125<x<1