Question

log6(x+1)+log 6(2x+1)<=1

Answer 1

$log_6(x+1)+log _6(2x+1) leq 1$
$log_6((x+1)(2x+1)) leq 1$
$(x+1)(2x+1) leq 6$
$2x^2+3x+1-6 leq 0$
$2x^2+3x-5 leq 0$
$(x-1)(x+2,5) leq 0$
ОДЗ:$left { {{x+1 textgreater 0} atop {2x+1 textgreater 0}} right. = textgreater left { {{x textgreater -1} atop {x textgreater -0,5}} right. = textgreater x textgreater -0,5$
x∈[1;∞)