Ln(x-4)=ln(x-1)-ln(x-5)

Solution for Ln(x-4)=ln(x-1)-ln(x-5) equation:

Simplifying
Ln(x + -4) = ln(x + -1) + -1ln(x + -5)

Reorder the terms:
nL(-4 + x) = ln(x + -1) + -1ln(x + -5)
(-4 * nL + x * nL) = ln(x + -1) + -1ln(x + -5)
(-4nL + nxL) = ln(x + -1) + -1ln(x + -5)

Reorder the terms:
-4nL + nxL = ln(-1 + x) + -1ln(x + -5)
-4nL + nxL = (-1 * ln + x * ln) + -1ln(x + -5)
-4nL + nxL = (-1ln + lnx) + -1ln(x + -5)

Reorder the terms:
-4nL + nxL = -1ln + lnx + -1ln(-5 + x)
-4nL + nxL = -1ln + lnx + (-5 * -1ln + x * -1ln)
-4nL + nxL = -1ln + lnx + (5ln + -1lnx)

Reorder the terms:
-4nL + nxL = -1ln + 5ln + lnx + -1lnx

Combine like terms: -1ln + 5ln = 4ln
-4nL + nxL = 4ln + lnx + -1lnx

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

Solving
-4nL + nxL = 4ln

Solving for variable 'n'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4l + -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 '(-4l + -4L + xL)' equal to zero and attempt to solve:

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

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

Solving
-4L + -4l + 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 + -4l + 4L + xL = 0 + 4L

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

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

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

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

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

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

Simplifying
0 = 4L + 4l + -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}