SOLUTION: ln(x+1)=ln(3x+1) - lnx solve exactly

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Question 33246This question is from textbook College Algebra
: ln(x+1)=ln(3x+1) - lnx
solve exactly This question is from textbook College Algebra

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
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