Log₂x-log₂y=1 ОДЗ: x>0 y>0
x²-y²=27
log₂(x/y)=1 x/y=2¹ x=2y x₁=2*3=6
(2y)²-y²=27 4y²-y²=27 3y²=27 I÷3 y²=9 y₁=3 y₂=-3 ∉ОДЗ
Ответ: х=6 у=3.
3*logx (y)+logy (x)=4 3*logx (y)+1/logx (y)=4 3*(logx (y))²-4*logx (y)+1=0 logx (y)=t
x-3y²=0 ОДЗ: x>0 y>0
3t²-4t+1=0 D=4
t₁=1 logx (y)=1 x=y x-3y²=0 y(3y-1)=0 y=0 ∉ОДЗ y₁=1/3 x₁=y₁=1/3
t₂=1/3 logx (y)=1/3 y=∛x x=y³ y³-3x²=0 y²(y-3)=0 y=0 ∉ОДЗ y₂=3 x₂=3³=27
Ответ: x₁=1/3 y₁=1/3 x₂=27 y₂=3.