ln(X-1)+ln(X-3)=ln(8)

Solution for ln(X-1)+ln(X-3)=ln(8) equation:

Simplifying
ln(X + -1) + ln(X + -3) = ln(8)

Reorder the terms:
ln(-1 + X) + ln(X + -3) = ln(8)
(-1 * ln + X * ln) + ln(X + -3) = ln(8)
(-1ln + lnX) + ln(X + -3) = ln(8)

Reorder the terms:
-1ln + lnX + ln(-3 + X) = ln(8)
-1ln + lnX + (-3 * ln + X * ln) = ln(8)
-1ln + lnX + (-3ln + lnX) = ln(8)

Reorder the terms:
-1ln + -3ln + lnX + lnX = ln(8)

Combine like terms: -1ln + -3ln = -4ln
-4ln + lnX + lnX = ln(8)

Combine like terms: lnX + lnX = 2lnX
-4ln + 2lnX = ln(8)

Reorder the terms for easier multiplication:
-4ln + 2lnX = 8ln

Solving
-4ln + 2lnX = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-4ln + -8ln + 2lnX = 8ln + -8ln

Combine like terms: -4ln + -8ln = -12ln
-12ln + 2lnX = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-12ln + 2lnX = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-6 + 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 '(-6 + X)' equal to zero and attempt to solve:

Simplifying
-6 + X = 0

Solving
-6 + X = 0

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

Add '6' to each side of the equation.
-6 + 6 + X = 0 + 6

Combine like terms: -6 + 6 = 0
0 + X = 0 + 6
X = 0 + 6

Combine like terms: 0 + 6 = 6
X = 6

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

Combine like terms: X + -1X = 0
0 = 6 + -1X

Simplifying
0 = 6 + -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.