Ln(x-4)=ln(x-8)-ln(x+1)

Solution for Ln(x-4)=ln(x-8)-ln(x+1) equation:

Simplifying
Ln(x + -4) = ln(x + -8) + -1ln(x + 1)

Reorder the terms:
nL(-4 + x) = ln(x + -8) + -1ln(x + 1)
(-4 * nL + x * nL) = ln(x + -8) + -1ln(x + 1)
(-4nL + nxL) = ln(x + -8) + -1ln(x + 1)

Reorder the terms:
-4nL + nxL = ln(-8 + x) + -1ln(x + 1)
-4nL + nxL = (-8 * ln + x * ln) + -1ln(x + 1)
-4nL + nxL = (-8ln + lnx) + -1ln(x + 1)

Reorder the terms:
-4nL + nxL = -8ln + lnx + -1ln(1 + x)
-4nL + nxL = -8ln + lnx + (1 * -1ln + x * -1ln)
-4nL + nxL = -8ln + lnx + (-1ln + -1lnx)

Reorder the terms:
-4nL + nxL = -8ln + -1ln + lnx + -1lnx

Combine like terms: -8ln + -1ln = -9ln
-4nL + nxL = -9ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-4nL + nxL = -9ln + 0
-4nL + nxL = -9ln

Solving
-4nL + nxL = -9ln

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '9ln' to each side of the equation.
-4nL + 9ln + nxL = -9ln + 9ln

Reorder the terms:
9ln + -4nL + nxL = -9ln + 9ln

Combine like terms: -9ln + 9ln = 0
9ln + -4nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(9l + -4L + xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0
Subproblem 2
Set the factor '(9l + -4L + xL)' equal to zero and attempt to solve:

Simplifying
9l + -4L + xL = 0

Reorder the terms:
-4L + 9l + xL = 0

Solving
-4L + 9l + xL = 0

Move all terms containing n to the left, all other terms to the right.

Add '4L' to each side of the equation.
-4L + 9l + 4L + xL = 0 + 4L

Reorder the terms:
-4L + 4L + 9l + xL = 0 + 4L

Combine like terms: -4L + 4L = 0
0 + 9l + xL = 0 + 4L
9l + xL = 0 + 4L
Remove the zero:
9l + xL = 4L

Add '-9l' to each side of the equation.
9l + -9l + xL = 4L + -9l

Combine like terms: 9l + -9l = 0
0 + xL = 4L + -9l
xL = 4L + -9l

Add '-1xL' to each side of the equation.
xL + -1xL = 4L + -9l + -1xL

Combine like terms: xL + -1xL = 0
0 = 4L + -9l + -1xL

Simplifying
0 = 4L + -9l + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}