23)
lg(x+6)-(1/2)*lg(2x-3)=2-lg25
2*lg(x+6)-lg(2x-3)=4-2*lg25
lg((x+6)^2)-lg(2x-3)=4-2*lg25
lg(((x+6)^2)/(2x-3))=4*lg10-2*lg25
lg(((x+6)^2)/(2x-3))=lg((10^4)/(25^2))
((x+6)^2)/(2x-3)=(10^4)/(25^2)
((x+6)^2)*(25^2)=(2x-3)*(10^4)
(x^2+12x+36)*(5^4)=(2x-3)*(2^4)*(5^4)
x^2+12x+36=(2x-3)*(2^4)
x^2+12x+36=32x-48
x^2-20x+84=0
 D=b^2-4ac=400-4*1*84=400-336=64=8^2

   

24)
1/(5-4lgx)+4/(1+lgx)=3
1+lgx+20-16lgx=3(5-4lgx)(1+lgx)
21-15lgx=3(5+lgx-4((lgx)^2))
21-15lgx=15+3lgx-12(lgx)^2
lgx=y
21-15y=15+3y-12y^2
12y^2-18y+6=0
2y^2-3y+1=0
D=9-8=1
y1=(3-1)/(2*2)=2/4=1/2
y2=(3+1)/(2*2)=4/4=1
lgx1=1/2
x1=
lgx2=1
x2=10=10

25)
2log2(x)+log(2^(1/2))(x)+log(1/2)(x)=9
2log2(x)+2log2(x)+log(2^(-1))(x)=9
4log2(x)-log2(x)=9
3log2(x)=9
log2(x)=3
x=2^3=8

26)
log3x+log9x+log27x=5,5
log3x+1/2*log3x+1/3*log3x=5,5
(6/6+3/6+2/6)*log3x=5,5
(11/6)*log3x=5,5
log3x=5,5*6/11
log3x=0,5*6
log3x=3
x=3^3
x=27

27)
2*log2(log2(x))+log(1/2)(log2(2*(2^(1/2))*x))=1
log2((log2(x))^2)-log2(log2(x*(2^(3/2))))=log2(2)
log2(((log2(x))^2)/(log2(x*(2^(3/2)))))=log2(2)
((log2(x))^2)/(log2(x*(2^(3/2))))=2
(log2(x))^2=2*log2(x*(2^(3/2)))
log2(x)*log2(x)=2*log2(x)+2*log2(2^(3/2))
log2(x)*log2(x)=2*log2(x)+2*3/2
log2(x)=y
y^2-2*y-3=0
D=4+4*3=16=4^2
y1=(2-4)/2=(-2)/2=-1
y2=(2+4)/2=6/2=3
log2(x1)=-1
x1=2^(-1)=1/2
log2(x2)=3
x2=2^3=8

Решение на фото, добавлю еще как решу