SOLUTION: please help me solve this ((( 1/2ln(x+3)-lnx=0 )))

Question 236522: please help me solve this ((( 1/2ln(x+3)-lnx=0 )))
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
1/2ln(x+3)-lnx=0

ln((x+3)^(1/2))-ln(x)=0

ln(sqrt(x+3))-ln(x)=0

ln(sqrt(x+3)/x)=0

sqrt(x+3)/x=1

sqrt(x+3)=x

x+3=x^2

x^2-x-3=0

x=1/2+(1/2)*sqrt(13) or x=1/2-(1/2)*sqrt(13)

Answer: Only solution is x = 1/2+(1/2)*sqrt(13) (other is extraneous)
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