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

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


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

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

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

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

Reorder the terms:
3ln = -2ln + lnx + lnx

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

Solving
3ln = -2ln + 2lnx

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.
3ln + 2ln = -2ln + 2ln + 2lnx

Combine like terms: 3ln + 2ln = 5ln
5ln = -2ln + 2ln + 2lnx

Combine like terms: -2ln + 2ln = 0
5ln = 0 + 2lnx
5ln = 2lnx

Add '-2lnx' to each side of the equation.
5ln + -2lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
5ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + -2x) = 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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Add '2x' to each side of the equation.
-2x + 2x = -5 + 2x

Combine like terms: -2x + 2x = 0
0 = -5 + 2x

Simplifying
0 = -5 + 2x

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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