Log2(3x+5)=3-log2(x+1)

[latex]log_2(3x+5)=3-log_2(x+1)[/latex] ОДЗ: [latex] \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} )[/latex] [latex]log_2(3x+5)+log_2(x+1)=3[/latex] [latex]log_2(3x+5)(x+1)=3[/latex] [latex](3x+5)(x+1)=2^3[/latex] [latex]3 x^{2} +8x+5=8[/latex] [latex]3 x^{2} +8x-3=0[/latex] [latex]D=100\ \textgreater \ 0[/latex] [latex]x_1=-3[/latex]- не подходит по ОДЗ [latex]x_2= \frac{1}{3} [/latex] Ответ: 1/3