Log3(7+2x)=log3(3-2x)+2

$\log_3(7+2x)=\log_3(3-2x)+2$

ОДЗ:

0} \atop {3-2x>0}} \right. \to \left \{ {{x>-3.5} \atop {x<1.5}} \right. " alt=" \left \{ {{7+2x>0} \atop {3-2x>0}} \right. \to \left \{ {{x>-3.5} \atop {x<1.5}} \right. " align="absmiddle" class="latex-formula">
Свойство логарифма $\log_a a^n=n$
$\log_3(7+2x)=\log_3(3-2x)+\log_33^2 \\ \log_3(7+2x)=\log_3(3^2(3-2x)) \\ 7+2x=9(3-2x) \\ 7+2x=27-18x \\ 20x=20 \\ x=20:20 \\ x=1$

Ответ: 1.