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

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


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

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

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

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

Combine like terms: 2ln + 1ln = 3ln
3ln + 2lnx + -3lnx = ln(x + -1)

Combine like terms: 2lnx + -3lnx = -1lnx
3ln + -1lnx = ln(x + -1)

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

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

Solving for variable 'l'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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