5.lg(3x²-2x+1)/lg(5x²-6x+1)⁵≥log₇⁵3/log₇3ОДЗ: 3x²-2x+1>0 D=-8 ⇒ 3x²-2x+1>05x²-6x+1>0 D=16x₁=0,2 x₂=1 ⇒(x-0,2)(x-1)>0 -∞__+___0,2___-___1___+___+∞ x∈(-∞;0,2)U(1;+∞).lg(3x²-2x+1)/(5*lg(5x²-6x+1))≥(1/5)*log₇3/log₇3lg(3x²-2x+1)/(5*lg(5x²-6x+1))≥1/5 |×5lg(3x²-2x+1)/(lg(5x²-6x+1)≥1log₍₅x²-₆x+₁₎(3x²-2x+1)≥13x²-2x+1≥(5x²-6x+1)¹3x²-2x+1≥5x²-6x+12x²-4x≤0 |÷2x²-2x≤0x*(x-2)≤0x₁=0 x-2=0x₂=2 ⇒-∞______+______0______-______2______+______+∞x∈(0;2).Согласно ОДЗ: x∈(0;0,2)U(1;2).Ответ: x∈(0;0,2)U(1;2).6.x²*log₁₆x-x*log₂x-log₁₆x⁵≥0 ОДЗ: x>0x²*log₂⁴(x)-x*log₂(x)-₂⁴(x⁵)≥0(1/4)*x²*log₂(x)-x*log₂(x)-(5/4)*log₂(x)≥0 |×4x²*log₂(x)-4*x*log₂(x)-5*log₂(x)≥0log₂(x)*(x²-4x-5)≥0log₂(x)=0x=2⁰x₁=1x²-4x-5=0 D=36 √D=6x₂=-1 x₃=5 ⇒(x-1)*(x+1)*(x-5)≥0Так как x>0 ⇒0_____+_____1_____-_____5_____+______+∞x∈(0;1)U(5;+∞).Ответ: x∈(0;1)U(5;+∞).