1) lg10x * lg0,1=3  

(lg10 +lgx) * (lg0,1 +lgx)=3

(1+lgx)*(-1+lgx)=3

(lgx)^2-1=3

(lgx)^2=4

lgx=2

x= 100

2)log0,5(2x-3)-1/2log0,5(2x-3)=0

log0,5(2x-3)-log0,5(2x-3)^1/2=0

log0,5(2x-3/(2x-3)^1/2)=0

log0,5(2x-3)^1/2=0

(2x-3)^1/2=1

2x-3=1

X=2

^ Знак степени