Solve the lograthmic function:

Question

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!

Answer 1

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.

Answer 2

Thank you soo much!