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

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


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

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

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

Solving
-2ln + 6lnx = -1ln + -1lnx

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.
-2ln + ln + 6lnx = -1ln + ln + -1lnx

Combine like terms: -2ln + ln = -1ln
-1ln + 6lnx = -1ln + ln + -1lnx

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

Add 'lnx' to each side of the equation.
-1ln + 6lnx + lnx = -1lnx + lnx

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

Combine like terms: -1lnx + lnx = 0
-1ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 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 '(-1 + 7x)' equal to zero and attempt to solve: Simplifying -1 + 7x = 0 Solving -1 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 7x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7x = 0 + 1 7x = 0 + 1 Combine like terms: 0 + 1 = 1 7x = 1 Add '-7x' to each side of the equation. 7x + -7x = 1 + -7x Combine like terms: 7x + -7x = 0 0 = 1 + -7x Simplifying 0 = 1 + -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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