№7
2log₅x + log₅y=1
log₅x - 2log₅y=8
log₅x² + log₅y=1
log₅x - log₅y²=8
log₅(x²y)=1
log₅(x/y²)=8
x²y=5
x/y²=5⁸
x=5⁸y²
(5⁸y²)²y=5
5¹⁶y⁵=5
5¹⁵y⁵=1
5³y=1
y=1/5³=1/125
x=5⁸/5⁶=5²=25
№5 log²₂x - log₂x=0
log₂x(log₂x-1)=0
log₂x₁=0 x₁=1
log₂x₂=1
x₂=2
№9
x+y=2
xy=-8
x=2-y
y(2-y)=-8
2y-y²=-8
y²-2y-8=0
D=2²+4*8=4+32=36
√D=6
y₁=(2-6)/2=-2
y₂=(2+6)/2=4
a=4
log₃(x+20)<4 и x+20>0, x>-20
x+20<3⁴<br>x<81-20=61<br>Ответ: -20
log²₃(27x) + 2log₃x=-7
(log₃(27x))² + 2log₃x=-7
(log₃27+log₃x)² + 2log₃x=-7
(3+log₃x)² + 2log₃x=-7
9+6log₃x+log²₃x + 2log₃x=-7
log²₃x+8log₃x+16=0
(log₃x+4)²=0
log₃x=-4
x=3⁻⁴=1/81
lg0,2 <0, поэтому<br>(3x-1) - (x+1)> 2
3x-1 - x-1> 2
2x-2> 2
x-1> 1
x>2