4)
log₄(x+12)*logx(2)=1 ОДЗ: x+12>0 x>-12 x>0 x≠1 ⇒ x∈(0;1)U(1;+∞).
(1/2)*log₂(x+12)/log₂x=1
log₂(x+12)=2*log₂x
log₂(x+12)=log₂x²
x+12=x²
x²-x-12=0 D=49
x₁=4 x₂=-3 ∉ОДЗ
Ответ: х=4.
5).
log₃log₀,₂log₃₂((x-1)/(x+5))>0
ОДЗ: (x-1)/(x+5)>0 -∞____+____-5____-____1____+_____+∞
x∈(-∞;-5)U(1;+∞)
log₃log₀,₂log₃₂((x-1)/(x+5))>log₃1
log₀,₂log₃₂((x-1)/(x+5)>1
log₀,₂log₃₂((x-1)/(x+5))>log₀,₂0,2
og₃₂((x-1)/(x+5))<0,2<br>(x-1)/(x+5)<32^(1/5)<br>(x-1)/(x+5)<2^(5*(1/5))<br>(x-1)/(x+5)<2<br>x-1<2*(x+5)<br>x-1<2x+10<br>x>-11
Ответ: x∈(-11;-5)U(1;+∞).