Question

Помогите пожалуйста с логарифмами!

Answer 1

3)log(3)x≤4
x>0 U x≤81
x∈(0;81]
4)log(4)(7-x)<3
7-x>0 U 7-x<64
x<7 U x>-57
x∈(-57;7)
5)y=lg(x²-7)
x²-7x>0
x(x-7)>0
x=0  x=7
x∈(-∞;0) U (7;∞)
6)log(3)(2x-1)<3
2x-1>0 U 2x-1<27
2x>1 U 2x<28
x>1/2 U x<14
x∈(1/2;14)
7)$16^{0,5log(4)10} =4 ^{log(4)10} =10$
8)(3log(7)2-log(7)24):(log*7)3+log(7)9)=log(7)[8/24]:log(7)27=
=log(7)1/3:log(7)27=log(27)1/3=-1/3