équation logarithme : Résoudre les équations: 2 ln(x+1)-ln(10x+10)=-ln2

C.E : x+1>0 <==>  x>-1

2ln(x+1) - ln(10x+10) = -ln 2
<==>  ln ( (x+1)² ) - ln (10x+10) = ln (1/2)
<==>  ln ( (x+1)²/10(x+1) ) =  ln (1/2)
<==>    (x+1)²/10(x+1) = 1/2
<==>    (x+1)² = 5(x+1)
<==>   x² +1 + 2x = 5x + 5
<==>  x² - 3x - 4 = 0
Δ:  9 - 4.(-4) = 9 + 16 = 25

==>  x = (3-5)/2  = -2/2 =- 1  (à écarter)  ou x = (3+5)/2 = 8/2=4

===>  Sol = {4}