2ln(3x-1)-ln(-x+4)=ln(x+2)

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Solution for 2ln(3x-1)-ln(-x+4)=ln(x+2) equation:


Simplifying
2ln(3x + -1) + -1ln(-1x + 4) = ln(x + 2)

Reorder the terms:
2ln(-1 + 3x) + -1ln(-1x + 4) = ln(x + 2)
(-1 * 2ln + 3x * 2ln) + -1ln(-1x + 4) = ln(x + 2)
(-2ln + 6lnx) + -1ln(-1x + 4) = ln(x + 2)

Reorder the terms:
-2ln + 6lnx + -1ln(4 + -1x) = ln(x + 2)
-2ln + 6lnx + (4 * -1ln + -1x * -1ln) = ln(x + 2)
-2ln + 6lnx + (-4ln + 1lnx) = ln(x + 2)

Reorder the terms:
-2ln + -4ln + 6lnx + 1lnx = ln(x + 2)

Combine like terms: -2ln + -4ln = -6ln
-6ln + 6lnx + 1lnx = ln(x + 2)

Combine like terms: 6lnx + 1lnx = 7lnx
-6ln + 7lnx = ln(x + 2)

Reorder the terms:
-6ln + 7lnx = ln(2 + x)
-6ln + 7lnx = (2 * ln + x * ln)
-6ln + 7lnx = (2ln + lnx)

Solving
-6ln + 7lnx = 2ln + lnx

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
-6ln + -2ln + 7lnx = 2ln + -2ln + lnx

Combine like terms: -6ln + -2ln = -8ln
-8ln + 7lnx = 2ln + -2ln + lnx

Combine like terms: 2ln + -2ln = 0
-8ln + 7lnx = 0 + lnx
-8ln + 7lnx = lnx

Add '-1lnx' to each side of the equation.
-8ln + 7lnx + -1lnx = lnx + -1lnx

Combine like terms: 7lnx + -1lnx = 6lnx
-8ln + 6lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-8ln + 6lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-4 + 3x) = 0

Ignore the factor 2.

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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Add '-3x' to each side of the equation. 3x + -3x = 4 + -3x Combine like terms: 3x + -3x = 0 0 = 4 + -3x Simplifying 0 = 4 + -3x 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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