Log(3x^2+8)=1+ Log(x\2+1)
All in base 10
log(3x^2+8) = 1+ log(x/2+1)
log(3x^2+8) = log10 + log(x/2+1)
log(3x^2+8) = log 10*(x/2+1)
log(3x^2+8) = log(5x+10)
3x^2+8 = 5x+10
3x^2-5x-2 = 0
(3x+1)(x-2) = 0
x = -1/3 or 2
All in base 10
log(3x^2+8) = log10 + log(x/2+1)
log(3x^2+8) = log 10*(x/2+1)
log(3x^2+8) = log(5x+10)
3x^2+8 = 5x+10
3x^2-5x-2 = 0
(3x+1)(x-2) = 0
x = -1/3 or 2