Question 33246
ln(x+1)=ln(3x+1) - lnx
ln(x+1)=ln{(3x+1)/x}...taking antilogs
x+1=(3x+1)/x
x(x+1)=3x+1
x^2+x-3x-1=0
x^2-2x-1=0..using quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (2 +- sqrt( (-2)^2-4*1*(-1) ))/(2*1) }}}
x=1+sqrt.(2)....or......1-sqrt.(2)..but since logof negative number does not exist...1-sqrt.(2) cannot be a solution.
so...x=1+sqrt.2=2.4142