## anonymous 3 years ago solve ln x= 1- ln (x+2)

1. anonymous

I get : lnx+ ln (x+2) ln(x)(x+2) ln (x^2 + 2x)= 1 e^1 = x^2 +2x ? and i need help from there on

2. zepdrix

I guess we would have to complete the square on the X's. Take half of the b term, and square it.$\large x^2+bx$

3. anonymous

so x^2+2x+1 = e ?

4. anonymous

but i get$x= \sqrt{e}-1$

5. anonymous

6. blurbendy

log(x) = 1 - log(x + 2) log(x) - 1 + log(x+2) = 0 log(x(x+2)) = 1 x(x+2) = e x^2 + 2x = e x^2 + 2x + 1 = 1 + e (x + 1)^2 = 1 + e x+1 = Sqrt[1 + e] or x + 1 = - Sqrt[1 + e} x = Sqrt[1 + e] - 1 or x + 1 = - Sqrt[1 + e] x = Sqrt[1 + e] - 1 or x = -1 -Sqrt[1 + e] Substitute back into the original equation, only 1 will be right x = Sqrt[1 + e] - 1

7. zepdrix

Ahhh sorry website froze :( erased all my stuff...

8. anonymous

thanks everyone and that sucks! @zepdrix :/ but thanks either way !

9. anonymous

ln(x)+ln(x+2)=1 ln(x(x+2))=ln(e) x(x+2)=e $x ^{2}+2x-e=0$ D=4+4e=4(1+e) =>sqrtD=2sqrt(1+e) x1=[-2+2sqrt(1-e)]/2=-1+sqrt(1+e)>0 accepted x2=[-2-2sqrt(1-e)]/2=-1-sqrt(1+e)<0 denied