Posted by **Laura Grace** on Wednesday, March 23, 2011 at 9:55pm.

Solve the lograthmic function:

ln(X+5) = ln(X-1) - ln(X+1)

The answer has no solution but I do not know how to come to that answer. Help is greatly appreciated!

- pre calc -
**Reiny**, Wednesday, March 23, 2011 at 10:06pm
ln(x+5) = ln[(x-1)/(x+1)]

x+5 = (x-1)/(x+1)

(x+5)(x+1) = x-1

x^2 + 6x + 5 = x-1

x^2 + 5x + 6 = 0

(x+2)(x+3) = 0

x = -2 or x=-3

but in ln(x-1), x-1>0 or x > 1

remember we can't take the log of a negative number and we would get ln(-3) and ln(-4) which would be undefined.

so neither of the solutions are valid, and

there is no solution to your equation.

- pre calc -
**Laura Grace**, Thursday, March 24, 2011 at 8:44pm
Thank you soo much!

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