Question

Помогите пж решить логарифмическое уравнение:
log(x+1)+log(x-1)=log3

Answer 1

ОДЗ :

$\left \{ {{x+1>0} \atop {x-1>0}} \right. \\\\\left \{ {{x>-1} \atop {x>1}} \right.\Rightarrow x>1$

$lg(x+1)+lg(x-1)=lg3\\\\lg(x+1)(x-1)=lg3\\\\lg(x^{2}-1)=lg3\\\\x^{2}-1=3\\\\x^{2}=4\\\\x_{1}=2\\\\x_{2}=-2-neyd\\\\Otvet:\boxed{2}$