ln(3x-1)+lnx=ln(1-3x)

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Solution for ln(3x-1)+lnx=ln(1-3x) equation: 


Simplifying
ln(3x + -1) + lnx = ln(1 + -3x)

Reorder the terms:
ln(-1 + 3x) + lnx = ln(1 + -3x)
(-1 * ln + 3x * ln) + lnx = ln(1 + -3x)
(-1ln + 3lnx) + lnx = ln(1 + -3x)

Combine like terms: 3lnx + lnx = 4lnx
-1ln + 4lnx = ln(1 + -3x)
-1ln + 4lnx = (1 * ln + -3x * ln)
-1ln + 4lnx = (1ln + -3lnx)

Solving
-1ln + 4lnx = 1ln + -3lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-1ln + -1ln + 4lnx = 1ln + -1ln + -3lnx

Combine like terms: -1ln + -1ln = -2ln
-2ln + 4lnx = 1ln + -1ln + -3lnx

Combine like terms: 1ln + -1ln = 0
-2ln + 4lnx = 0 + -3lnx
-2ln + 4lnx = -3lnx

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

Combine like terms: 4lnx + 3lnx = 7lnx
-2ln + 7lnx = -3lnx + 3lnx

Combine like terms: -3lnx + 3lnx = 0
-2ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 7x) = 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 '(-2 + 7x)' equal to zero and attempt to solve:

Simplifying
-2 + 7x = 0

Solving
-2 + 7x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7x = 0 + 2
7x = 0 + 2

Combine like terms: 0 + 2 = 2
7x = 2

Add '-7x' to each side of the equation.
7x + -7x = 2 + -7x

Combine like terms: 7x + -7x = 0
0 = 2 + -7x

Simplifying
0 = 2 + -7x

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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