Question

решить уравнение log (127+x³)-3log(x+1)=0

Answer 1

log(127+x³)-3*log(x+1)=0
ОДЗ:
$left { {{127+ x^{3} textgreater 0} atop {x+1 textgreater 0}} right. , left { {{ x^{3} textgreater -127 } atop {x textgreater -1}} right. , left { {{x textgreater sqrt[3]{-127} } atop {x textgreater -1}} right.$
x>-1. x∈(-1;∞)
log(127+x³)=3*log(x+1)
log(127+x³)=log(x+1)³
127+x³=(x+1)³
127+x³=x³+3x²+3x+1
3x²+3x-126=0 |:3
x²+x-42=0
D=169
x₁=-7, x₂=6
-7∉(-1;∞). => x=-7 посторонний корень

ответ: x=6