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

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Solution for ln(3x-1)-ln(x+2)=ln(2) equation: 


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

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

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

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

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

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

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

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

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

Combine like terms: 2ln + -2ln = 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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