Question

2lgx-lg(x+3)=lg2
Помогите пожалуйста решить.

Answer 1

$2lgx-lg(x+3)=lg2$

ОДЗ:  $\left \{ {{x\ \textgreater \ 0} \atop {x+3\ \textgreater \ 0}} \right. =\ \textgreater \ \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ -3}} \right. =\ \textgreater \ x\ \textgreater \ 0$

$lgx^2-lg(x+3)=lg2\\lg\frac{x^2}{x+3}=lg2\\\frac{x^2}{x+3}=2\\\frac{x^2}{x+3}-2=0\\\frac{x^2-2x-6}{x+3}=0\\\\D=2^2+4*6=4+24=28\\\\x_1=\frac{2+\sqrt{28}}2=\frac{2+2\sqrt{7}}2=1+\sqrt7\\\\x_2=\frac{2-\sqrt{28}}2=\frac{2-2\sqrt{7}}2=1-\sqrt7\ \textless \ 0\notin (x\ \textgreater \ 0)$

Ответ:  $x=1+\sqrt7$