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elizaveta2000ku
@elizaveta2000ku
July 2022
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Помогите, пожалуйста, с примерами:
1) lg (3х2 + 7) - lg (93х – 2) = 1
2) lg(х – 1) + lg(х + 1) = 3 lg 2 + lg(х – 2)
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sangers1959
Verified answer
1) lg(3x²+7)-lg(93x-2)=1 ОДЗ: 3х₁+7>0 x>-7/3 93x-2>0 x>2/93 ⇒x>2/93≈0,022
lg(3x²+7)/(93x-2)=1
(3x²+7)/(93x-2)=10¹
3x²+7=930x-20
3x²-930x+27=0 D=864576 √D=4√1501
x₁=155+4√1501≈310
x₂=155-4√1501≈=0,03.
2) lg(x-1)+lg(x+1)=3*lg2+lg(x-2) ОДЗ: x-1>0 x+1>0 x-2>0 ⇒ x>2
(x-1)((x+1)=2³*(x-2)
x²-1=8x-16
x²-8x+15=0 D=4 √D=2
x₁=5 x₂=3
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Answers & Comments
Verified answer
1) lg(3x²+7)-lg(93x-2)=1 ОДЗ: 3х₁+7>0 x>-7/3 93x-2>0 x>2/93 ⇒x>2/93≈0,022lg(3x²+7)/(93x-2)=1
(3x²+7)/(93x-2)=10¹
3x²+7=930x-20
3x²-930x+27=0 D=864576 √D=4√1501
x₁=155+4√1501≈310
x₂=155-4√1501≈=0,03.
2) lg(x-1)+lg(x+1)=3*lg2+lg(x-2) ОДЗ: x-1>0 x+1>0 x-2>0 ⇒ x>2
(x-1)((x+1)=2³*(x-2)
x²-1=8x-16
x²-8x+15=0 D=4 √D=2
x₁=5 x₂=3