ln(x-2)=lnx-ln(x-2)

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


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

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

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

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

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

Solving
-2ln + lnx = 2ln

Solving for variable 'l'.

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

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

Combine like terms: -2ln + -2ln = -4ln
-4ln + lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
-4ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + x) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Add '-1x' to each side of the equation.
x + -1x = 4 + -1x

Combine like terms: x + -1x = 0
0 = 4 + -1x

Simplifying
0 = 4 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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