pre calc
posted by Laura Grace on .
Solve the lograthmic function:
ln(X+5) = ln(X1)  ln(X+1)
The answer has no solution but I do not know how to come to that answer. Help is greatly appreciated!

ln(x+5) = ln[(x1)/(x+1)]
x+5 = (x1)/(x+1)
(x+5)(x+1) = x1
x^2 + 6x + 5 = x1
x^2 + 5x + 6 = 0
(x+2)(x+3) = 0
x = 2 or x=3
but in ln(x1), x1>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. 
Thank you soo much!