Question

Решите уравнение
㏒3(x+1)+㏒3(x+3)=1

Answer 1

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