Решение
<span>Log11(x+4)+log11(x-2)=log11(x-6)
ОДЗ: x + 4 > 0, x > - 4
x - 2 > 0, x > 2
x - 6 > 0, x > 6
ОДЗ: </span>∈ (6; + ∞)
log₁₁[(x + 4)*(x - 2)] = log₁₁(x - 6)
<span>[(x + 4)*(x - 2)] = x - 6
x</span>² + 2x - 8 - x + 6 = 0
x² + x - 2 = 0
x₁ = - 2 ∉ <span> (6; + ∞)</span>
x = 1 ∉ <span> (6; + ∞)
</span>уравнение решений не имеет
Log5 x + log5 y =1 , x bolše čem 0, y bolše čem 0
2ˇ(x+y-3)=8
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log5 (xy)=1
2ˇ(x+y-3)=2³
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xy=5ˇ1
x+y-3=2
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xy=5
x+y=5
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y=5-x
x(5-x)=5
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y=5-x
5x-x²=5
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y=5-x
x²-5x+5=0, D=25-20=5 , √D=√5)
a)x1=(5+√5)/2 , y1=5-(5+√5)/2=5-2,5-√5/2=2,5-√5/2
b)x2=(5-√5)/2 , y2=5-(5-√5)/2=5-2,5+√5/2=2,5+√5/2