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

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

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

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

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

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

Reorder the terms for easier multiplication:
2lmx + -3ln = 12ln

Solving
2lmx + -3ln = 12ln

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
2lmx + -3ln + -12ln = 12ln + -12ln

Combine like terms: -3ln + -12ln = -15ln
2lmx + -15ln = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
2lmx + -15ln = 0

Factor out the Greatest Common Factor (GCF), 'l'.
l(2mx + -15n) = 0

Subproblem 1
Set the factor 'l' equal to zero and attempt to solve:

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0
Subproblem 2
Set the factor '(2mx + -15n)' equal to zero and attempt to solve:

Simplifying
2mx + -15n = 0

Solving
2mx + -15n = 0

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

Add '-2mx' to each side of the equation.
2mx + -2mx + -15n = 0 + -2mx

Combine like terms: 2mx + -2mx = 0
0 + -15n = 0 + -2mx
-15n = 0 + -2mx
Remove the zero:
-15n = -2mx

Add '15n' to each side of the equation.
-15n + 15n = -2mx + 15n

Combine like terms: -15n + 15n = 0
0 = -2mx + 15n

Simplifying
0 = -2mx + 15n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
l = {0}