pre calc

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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 -

    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 -

    Thank you soo much!

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