Răspuns:
Explicație pas cu pas:
DVA: [tex]\left \{ {{x+1>0} \atop {3x-7>0}} \right. ~~\left \{ {{x>-1} \atop {x>7/3}} \right.~deci~x>7/3.\\log_{5}(x+1)-2*log_{5}(3x-7)=-1,~log_{5}(x+1)+1=2*log_{5}(3x-7), ~log_{5}(x+1)+log_{5}5=log_{5}(3x-7)^{2},~log_{5}[(x+1)*5]=log_{5}(3x-7)^{2}[/tex]
⇒5(x+1)=(3x-7)² ⇒5x+5=9x²-42x+49 ⇒9x²-47x+44=0
Δ=(-47)²-4·9·44=625, x1=(47-25)/18=22/18∉DVA
x2=(47+25)/18=72/18=4∈DVA
Raspuns: S={4}.
