SOLUTION: Solve for x: ln(x+1)-ln(x-2)=lnx

Question 64539: Solve for x:
ln(x+1)-ln(x-2)=lnx
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
ln(x+1)-ln(x-2)=lnx
Since lna - lnb = ln(a/b)
=ln[(x+1)/(x-2)]=lnx
If these ln's are equal the arguments must be equal:
(x+1)/(x-2)=x
Cross-multiply to get:
x+1=x^2-2x
x^2-3x-1=0
Using the quadratic formula you get:
x=[3+-sqrt(9-4(-1)]/2
x=[3+-sqrt13]/2
x=(3/2)1+(1/2)sqrt13 is the only solution as the alternate x=(3/2)-(1/2)sqrt13 is negative and cannot satisfy the original equation because
the original equation has a term lnx and ln(a negative number) is
not a defined number.
Let me know if this helps.
Cheers,
Stan H.

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