Question

Log5(4x+1)+log5(x+1)=log5 35-1

Answer 1

$log5(4x+1)+log5(x+1)=log5(35)-1$
$ODZ: x textgreater - frac{1}{4}$
$log5(4x+1)+log5(x+1)=log5(35)-log5(5)$
$log5(4 x^{2} +x+4x+1)=log5(35/5)=log5(7)$
$4x^{2} +5x+1=7$
$4 x^{2} +5x-6=0$
$D=25+96=121$
$x1= frac{-5+11}{8} =0,75$
$x2= frac{-5-11}{8} =-2$
$OTBET: x=0,75$