Question

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

Answer 1

log3(7+2x)=log3(3-2x)+log3(9)
log3(7+2x)=log3((3-2x)*9)
7+2x=27-18x
20x=20
x=1

Answer 2

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

ОДЗ: $left { {{7+2x>0} atop {3-2x>0}} right. to left { {{x>-3.5} atop {x<1.5}} right.$
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.