Question

log2(3x+5)=3-log2(x+1)

Answer 1

$log_2(3x+5)=3-log_2(x+1)$
ОДЗ: $\left \{ {{3x+5\ \textgreater \ 0} \atop {x+1\ \textgreater \ 0}} \right. ; \left \{ {{x\ \textgreater \ - \frac{5}{3} } \atop {x\ \textgreater \ -1}} \right. \ \textless \ =\ \textgreater \ (-1;+ \infty} )$
$log_2(3x+5)+log_2(x+1)=3$
$log_2(3x+5)(x+1)=3$
$(3x+5)(x+1)=2^3$
$3 x^{2} +8x+5=8$
$3 x^{2} +8x-3=0$
$D=100\ \textgreater \ 0$
$x_1=-3$- не подходит по ОДЗ
$x_2= \frac{1}{3}$
Ответ: 1/3