Question

d) log5 (x+1) – 2 log5 (3x – 7)=-1;​

Answer 1

Răspuns:

Explicație pas cu pas:

DVA: $\left \{ {{x+1>0} \atop {3x-7>0}} \right. ~~\left \{ {{x>-1} \atop {x>7/3}} \right.~deci~x>7/3.\\log_{5}(x+1)-2*log_{5}(3x-7)=-1,~log_{5}(x+1)+1=2*log_{5}(3x-7), ~log_{5}(x+1)+log_{5}5=log_{5}(3x-7)^{2},~log_{5}[(x+1)*5]=log_{5}(3x-7)^{2}$

⇒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}.