Ln(x-4)=ln(x+6)-lnx

Solution for Ln(x-4)=ln(x+6)-lnx equation:

Simplifying
Ln(x + -4) = ln(x + 6) + -1lnx

Reorder the terms:
nL(-4 + x) = ln(x + 6) + -1lnx
(-4 * nL + x * nL) = ln(x + 6) + -1lnx
(-4nL + nxL) = ln(x + 6) + -1lnx

Reorder the terms:
-4nL + nxL = ln(6 + x) + -1lnx
-4nL + nxL = (6 * ln + x * ln) + -1lnx
-4nL + nxL = (6ln + lnx) + -1lnx

Combine like terms: lnx + -1lnx = 0
-4nL + nxL = 6ln + 0
-4nL + nxL = 6ln

Solving
-4nL + nxL = 6ln

Solving for variable 'n'.

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

Add '-6ln' to each side of the equation.
-4nL + -6ln + nxL = 6ln + -6ln

Reorder the terms:
-6ln + -4nL + nxL = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-6ln + -4nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6l + -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 '(-6l + -4L + xL)' equal to zero and attempt to solve:

Simplifying
-6l + -4L + xL = 0

Reorder the terms:
-4L + -6l + xL = 0

Solving
-4L + -6l + 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 + -6l + 4L + xL = 0 + 4L

Reorder the terms:
-4L + 4L + -6l + xL = 0 + 4L

Combine like terms: -4L + 4L = 0
0 + -6l + xL = 0 + 4L
-6l + xL = 0 + 4L
Remove the zero:
-6l + xL = 4L

Add '6l' to each side of the equation.
-6l + 6l + xL = 4L + 6l

Combine like terms: -6l + 6l = 0
0 + xL = 4L + 6l
xL = 4L + 6l

Add '-1xL' to each side of the equation.
xL + -1xL = 4L + 6l + -1xL

Combine like terms: xL + -1xL = 0
0 = 4L + 6l + -1xL

Simplifying
0 = 4L + 6l + -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}