Question

log5(x+1) - log5(1-x) = log5(2x+3)

Answer 1

ОДЗ
{x+1>0⇒x>-1
{1-x>0⇒x<1
{2x+3>0⇒x>-1.5
x∈(-1;1)
log(5)[(x+1)/(1-x)]=log(5)(2x+3)
(x+1)/(1-x)=2x+3
(2x+3)(1-x)-(x+1)=0
2x-2x²+3-3x-x-1=0
2x²+2x-2=0
x²+x-1=0
D=1+4=5
x1=(-1-√5)/2∉ОДЗ
х2=(-1+√5)/2