Ln(2)+ln(x)=ln(6)+ln(3x-2)

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

Simplifying
Ln(2) + ln(x) = ln(6) + ln(3x + -2)

Reorder the terms for easier multiplication:
2nL + ln(x) = ln(6) + ln(3x + -2)

Multiply ln * x
2nL + lnx = ln(6) + ln(3x + -2)

Reorder the terms:
lnx + 2nL = ln(6) + ln(3x + -2)

Reorder the terms for easier multiplication:
lnx + 2nL = 6ln + ln(3x + -2)

Reorder the terms:
lnx + 2nL = 6ln + ln(-2 + 3x)
lnx + 2nL = 6ln + (-2 * ln + 3x * ln)
lnx + 2nL = 6ln + (-2ln + 3lnx)

Combine like terms: 6ln + -2ln = 4ln
lnx + 2nL = 4ln + 3lnx

Solving
lnx + 2nL = 4ln + 3lnx

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
lnx + -4ln + 2nL = 4ln + -4ln + 3lnx

Reorder the terms:
-4ln + lnx + 2nL = 4ln + -4ln + 3lnx

Combine like terms: 4ln + -4ln = 0
-4ln + lnx + 2nL = 0 + 3lnx
-4ln + lnx + 2nL = 3lnx

Add '-3lnx' to each side of the equation.
-4ln + lnx + -3lnx + 2nL = 3lnx + -3lnx

Combine like terms: lnx + -3lnx = -2lnx
-4ln + -2lnx + 2nL = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-4ln + -2lnx + 2nL = 0

Add '-2nL' to each side of the equation.
-4ln + -2lnx + 2nL + -2nL = 0 + -2nL

Combine like terms: 2nL + -2nL = 0
-4ln + -2lnx + 0 = 0 + -2nL
-4ln + -2lnx = 0 + -2nL
Remove the zero:
-4ln + -2lnx = -2nL

Combine like terms: -2nL + 2nL = 0
-4ln + -2lnx + 2nL = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(-2l + -1lx + L) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-2l + -1lx + L)' equal to zero and attempt to solve:

Simplifying
-2l + -1lx + L = 0

Reorder the terms:
L + -2l + -1lx = 0

Solving
L + -2l + -1lx = 0

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

Add '-1L' to each side of the equation.
L + -2l + -1L + -1lx = 0 + -1L

Reorder the terms:
L + -1L + -2l + -1lx = 0 + -1L

Combine like terms: L + -1L = 0
0 + -2l + -1lx = 0 + -1L
-2l + -1lx = 0 + -1L
Remove the zero:
-2l + -1lx = -1L

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.