Ln(3x)=ln(6)

Solution for Ln(3x)=ln(6) equation:

Simplifying
Ln(3x) = ln(6)

Remove parenthesis around (3x)
nL * 3x = ln(6)

Reorder the terms for easier multiplication:
3nL * x = ln(6)

Multiply nL * x
3nxL = ln(6)

Reorder the terms for easier multiplication:
3nxL = 6ln

Solving
3nxL = 6ln

Solving for variable 'n'.

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

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

Combine like terms: 6ln + -6ln = 0
-6ln + 3nxL = 0

Factor out the Greatest Common Factor (GCF), '3n'.
3n(-2l + xL) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

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

Simplifying
-2l + xL = 0

Solving
-2l + xL = 0

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

Add '2l' to each side of the equation.
-2l + 2l + xL = 0 + 2l

Combine like terms: -2l + 2l = 0
0 + xL = 0 + 2l
xL = 0 + 2l
Remove the zero:
xL = 2l

Add '-1xL' to each side of the equation.
xL + -1xL = 2l + -1xL

Combine like terms: xL + -1xL = 0
0 = 2l + -1xL

Simplifying
0 = 2l + -1xL

The solution to this equation could not be determined.

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