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

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

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

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

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

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

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

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

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

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

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

Solving
-2ln + 2lnx = 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.
-2ln + -2ln + 2lnx = 2ln + -2ln + lnx

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

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

Add '-1lnx' to each side of the equation.
-4ln + 2lnx + -1lnx = lnx + -1lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + x) = 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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

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

Combine like terms: x + -1x = 0
0 = 4 + -1x

Simplifying
0 = 4 + -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.