ln(2v+2)=ln(3v-6)

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Solution for ln(2v+2)=ln(3v-6) equation: 


Simplifying
ln(2v + 2) = ln(3v + -6)

Reorder the terms:
ln(2 + 2v) = ln(3v + -6)
(2 * ln + 2v * ln) = ln(3v + -6)
(2ln + 2lnv) = ln(3v + -6)

Reorder the terms:
2ln + 2lnv = ln(-6 + 3v)
2ln + 2lnv = (-6 * ln + 3v * ln)
2ln + 2lnv = (-6ln + 3lnv)

Solving
2ln + 2lnv = -6ln + 3lnv

Solving for variable 'l'.

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

Add '6ln' to each side of the equation.
2ln + 6ln + 2lnv = -6ln + 6ln + 3lnv

Combine like terms: 2ln + 6ln = 8ln
8ln + 2lnv = -6ln + 6ln + 3lnv

Combine like terms: -6ln + 6ln = 0
8ln + 2lnv = 0 + 3lnv
8ln + 2lnv = 3lnv

Add '-3lnv' to each side of the equation.
8ln + 2lnv + -3lnv = 3lnv + -3lnv

Combine like terms: 2lnv + -3lnv = -1lnv
8ln + -1lnv = 3lnv + -3lnv

Combine like terms: 3lnv + -3lnv = 0
8ln + -1lnv = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -1v) = 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 '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1v = 0 + -8
-1v = 0 + -8

Combine like terms: 0 + -8 = -8
-1v = -8

Add 'v' to each side of the equation.
-1v + v = -8 + v

Combine like terms: -1v + v = 0
0 = -8 + v

Simplifying
0 = -8 + v

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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