Question

Решите уравнение
log3(x+2) + log3(5x+4)=3

Answer 1

ОДЗ:
$left { {{x+2 textgreater 0} atop {5x+4 textgreater 0}} right. textless = textgreater left { {{x textgreater -2} atop {x textgreater -0.8}} right. textless = textgreater x textgreater -0.8$

$log _{3} (x+2) + log_{3} (5x+4)=3 \ log_{3} (x+2)(5x+4)=3 \ 3 ^{3} =(x+2)(5x+4) \ 5 x^{2} +4x+10x+8=27 \ 5 x^{2} +14x-19=0 \ D=196+380=576=24 ^{2} \ x= frac{-14+24}{10} =1 \ x= frac{-14-24}{10}=-3.8$
- не удовл. ОДЗ
отв:х=1