ln(3x)=ln(12)-ln(2)

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Solution for ln(3x)=ln(12)-ln(2) equation: 


Simplifying
ln(3x) = ln(12) + -1ln(2)

Remove parenthesis around (3x)
ln * 3x = ln(12) + -1ln(2)

Reorder the terms for easier multiplication:
3ln * x = ln(12) + -1ln(2)

Multiply ln * x
3lnx = ln(12) + -1ln(2)

Reorder the terms for easier multiplication:
3lnx = 12ln + -1ln(2)

Reorder the terms for easier multiplication:
3lnx = 12ln + -1 * 2ln

Multiply -1 * 2
3lnx = 12ln + -2ln

Combine like terms: 12ln + -2ln = 10ln
3lnx = 10ln

Solving
3lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-10ln + 3lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-10ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-10 + 3x) = 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 '(-10 + 3x)' equal to zero and attempt to solve:

Simplifying
-10 + 3x = 0

Solving
-10 + 3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + 3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3x = 0 + 10
3x = 0 + 10

Combine like terms: 0 + 10 = 10
3x = 10

Add '-3x' to each side of the equation.
3x + -3x = 10 + -3x

Combine like terms: 3x + -3x = 0
0 = 10 + -3x

Simplifying
0 = 10 + -3x

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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