2ln(x+1)=ln(-2x+6)

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Solution for 2ln(x+1)=ln(-2x+6) equation:


Simplifying
2ln(x + 1) = ln(-2x + 6)

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

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

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

Solving for variable 'l'.

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

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

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

Combine like terms: 6ln + -6ln = 0
-4ln + 2lnx = 0 + -2lnx
-4ln + 2lnx = -2lnx

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

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

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

Factor out the Greatest Common Factor (GCF), '4ln'.
4ln(-1 + x) = 0

Ignore the factor 4.

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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -1x 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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