Ln(x-2)=ln(x)-ln(2)

Solution for Ln(x-2)=ln(x)-ln(2) equation:

Simplifying
Ln(x + -2) = ln(x) + -1ln(2)

Reorder the terms:
nL(-2 + x) = ln(x) + -1ln(2)
(-2 * nL + x * nL) = ln(x) + -1ln(2)
(-2nL + nxL) = ln(x) + -1ln(2)

Multiply ln * x
-2nL + nxL = lnx + -1ln(2)

Reorder the terms for easier multiplication:
-2nL + nxL = lnx + -1 * 2ln

Multiply -1 * 2
-2nL + nxL = lnx + -2ln

Reorder the terms:
-2nL + nxL = -2ln + lnx

Solving
-2nL + nxL = -2ln + lnx

Solving for variable 'n'.

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

Add '2ln' to each side of the equation.
-2nL + 2ln + nxL = -2ln + 2ln + lnx

Reorder the terms:
2ln + -2nL + nxL = -2ln + 2ln + lnx

Combine like terms: -2ln + 2ln = 0
2ln + -2nL + nxL = 0 + lnx
2ln + -2nL + nxL = lnx

Add '-1lnx' to each side of the equation.
2ln + -2nL + -1lnx + nxL = lnx + -1lnx

Reorder the terms:
2ln + -1lnx + -2nL + nxL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
2ln + -1lnx + -2nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(2l + -1lx + -2L + 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 '(2l + -1lx + -2L + xL)' equal to zero and attempt to solve:

Simplifying
2l + -1lx + -2L + xL = 0

Reorder the terms:
-2L + 2l + -1lx + xL = 0

Solving
-2L + 2l + -1lx + xL = 0

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

Add '2L' to each side of the equation.
-2L + 2l + -1lx + 2L + xL = 0 + 2L

Reorder the terms:
-2L + 2L + 2l + -1lx + xL = 0 + 2L

Combine like terms: -2L + 2L = 0
0 + 2l + -1lx + xL = 0 + 2L
2l + -1lx + xL = 0 + 2L
Remove the zero:
2l + -1lx + xL = 2L

Add '-2l' to each side of the equation.
2l + -1lx + -2l + xL = 2L + -2l

Reorder the terms:
2l + -2l + -1lx + xL = 2L + -2l

Combine like terms: 2l + -2l = 0
0 + -1lx + xL = 2L + -2l
-1lx + xL = 2L + -2l

Add 'lx' to each side of the equation.
-1lx + lx + xL = 2L + -2l + lx

Combine like terms: -1lx + lx = 0
0 + xL = 2L + -2l + lx
xL = 2L + -2l + lx

Add '-1xL' to each side of the equation.
xL + -1xL = 2L + -2l + lx + -1xL

Combine like terms: xL + -1xL = 0
0 = 2L + -2l + lx + -1xL

Simplifying
0 = 2L + -2l + lx + -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}