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Nameles
@Nameles
November 2021
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Помогите решить логарифмы пожалуйста
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oganesbagoyan
Verified answer
Loq(2) 4x + Loq(2) (x - 7,5) =1 ;
ОДЗ : { 4x >0 ; x - 7,5 > 0. x∈
(7,5; ∞)
.
Loq(2) 4x(x- 7,5) = Loq(2) 2 ;
4x(x -7,5) =2 ;
2x(x -7,5) =1 ;
2x² - 15x -1 =0 ;
x₁ =(15 -√233)/4 ∉ ОДЗ.
x₂ =
(15+√233)/4
≈7,57 > 7,5.
ответ :
(15+√233)/4
.
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Answers & Comments
Verified answer
Loq(2) 4x + Loq(2) (x - 7,5) =1 ;ОДЗ : { 4x >0 ; x - 7,5 > 0. x∈(7,5; ∞).
Loq(2) 4x(x- 7,5) = Loq(2) 2 ;
4x(x -7,5) =2 ;
2x(x -7,5) =1 ;
2x² - 15x -1 =0 ;
x₁ =(15 -√233)/4 ∉ ОДЗ.
x₂ =(15+√233)/4 ≈7,57 > 7,5.
ответ : (15+√233)/4 .