Ln(3)=ln(3x+2)

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

Simplifying
Ln(3) = ln(3x + 2)

Reorder the terms for easier multiplication:
3nL = ln(3x + 2)

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

Solving
3nL = 2ln + 3lnx

Solving for variable 'n'.

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

Add '-2ln' to each side of the equation.
-2ln + 3nL = 2ln + -2ln + 3lnx

Combine like terms: 2ln + -2ln = 0
-2ln + 3nL = 0 + 3lnx
-2ln + 3nL = 3lnx

Add '-3lnx' to each side of the equation.
-2ln + -3lnx + 3nL = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-2ln + -3lnx + 3nL = 0

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

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 + -3lx + 3L)' equal to zero and attempt to solve:

Simplifying
-2l + -3lx + 3L = 0

Reorder the terms:
3L + -2l + -3lx = 0

Solving
3L + -2l + -3lx = 0

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

Add '-3L' to each side of the equation.
3L + -2l + -3L + -3lx = 0 + -3L

Reorder the terms:
3L + -3L + -2l + -3lx = 0 + -3L

Combine like terms: 3L + -3L = 0
0 + -2l + -3lx = 0 + -3L
-2l + -3lx = 0 + -3L
Remove the zero:
-2l + -3lx = -3L

Add '2l' to each side of the equation.
-2l + 2l + -3lx = -3L + 2l

Combine like terms: -2l + 2l = 0
0 + -3lx = -3L + 2l
-3lx = -3L + 2l

Add '3lx' to each side of the equation.
-3lx + 3lx = -3L + 2l + 3lx

Combine like terms: -3lx + 3lx = 0
0 = -3L + 2l + 3lx

Simplifying
0 = -3L + 2l + 3lx

The solution to this equation could not be determined.

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