log(3) (x+1) + log(3) (x+3)= 1. Created by MK20. algebra-ru

одз:решаем:Ответ: x=0

log(3) (x+1) + log(3) (x+3)= 1...

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$\log_3(x+1)+\log_3(x+3)=1$
одз:
$\left \{ {{x+1\ \textgreater \ 0} \atop {x+3\ \textgreater \ 0}} \right. \Rightarrow \left \{ {{x\ \textgreater \ -1} \atop {x\ \textgreater \ -3}} \right. \Rightarrow x \in (-1;+\infty)$
решаем:
$\log_3((x+1)(x+3))=1
\\(x+1)(x+3)=3^1
\\x^2+3x+x+3=3
\\x^2+4x=0
\\x(x+4)=0
\\x_1=0
\\x_2=-4\notin (-1;+\infty)$
Ответ: x=0

2 votes Thanks 4

Universalka

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ОДЗ: x + 1 > 0 ⇒ x > - 1
x + 3 > 0 ⇒ x > - 3
Окончательно : x > - 1

$log _{3}(x+1)+log _{3}(x+3)=1\\\\log _{3}(x+1)(x+3)=1\\\\(x+1)(x+3)=3\\\\ x^{2} +4x=0\\\\x(x+4)=0\\\\ x_{1}=0 , x_{2}=-4$
x₂ = - 4 - не подходит
Ответ : 0

2 votes Thanks 1

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