ln(2x)-ln(x-2)=ln(3)

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Solution for ln(2x)-ln(x-2)=ln(3) equation: 


Simplifying
ln(2x) + -1ln(x + -2) = ln(3)

Remove parenthesis around (2x)
ln * 2x + -1ln(x + -2) = ln(3)

Reorder the terms for easier multiplication:
2ln * x + -1ln(x + -2) = ln(3)

Multiply ln * x
2lnx + -1ln(x + -2) = ln(3)

Reorder the terms:
2lnx + -1ln(-2 + x) = ln(3)
2lnx + (-2 * -1ln + x * -1ln) = ln(3)
2lnx + (2ln + -1lnx) = ln(3)

Reorder the terms:
2ln + 2lnx + -1lnx = ln(3)

Combine like terms: 2lnx + -1lnx = 1lnx
2ln + 1lnx = ln(3)

Reorder the terms for easier multiplication:
2ln + 1lnx = 3ln

Solving
2ln + 1lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
2ln + -3ln + 1lnx = 3ln + -3ln

Combine like terms: 2ln + -3ln = -1ln
-1ln + 1lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-1ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

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

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

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

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

Simplifying
0 = 1 + -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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