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

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


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

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

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

Solving for variable 'l'.

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

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

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

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

Add 'lnx' to each side of the equation.
-2ln + lnx + lnx = -1lnx + lnx

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

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

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-1 + x) = 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 '(-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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