ln(x+1)+ln(x-5)=12

Solution for ln(x+1)+ln(x-5)=12 equation:

Simplifying
ln(x + 1) + ln(x + -5) = 12

Reorder the terms:
ln(1 + x) + ln(x + -5) = 12
(1 * ln + x * ln) + ln(x + -5) = 12
(1ln + lnx) + ln(x + -5) = 12

Reorder the terms:
1ln + lnx + ln(-5 + x) = 12
1ln + lnx + (-5 * ln + x * ln) = 12
1ln + lnx + (-5ln + lnx) = 12

Reorder the terms:
1ln + -5ln + lnx + lnx = 12

Combine like terms: 1ln + -5ln = -4ln
-4ln + lnx + lnx = 12

Combine like terms: lnx + lnx = 2lnx
-4ln + 2lnx = 12

Solving
-4ln + 2lnx = 12

Solving for variable 'l'.

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

Reorder the terms:
-12 + -4ln + 2lnx = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -4ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -2ln + lnx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -2ln + lnx)' equal to zero and attempt to solve:

Simplifying
-6 + -2ln + lnx = 0

Solving
-6 + -2ln + lnx = 0

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

Add '6' to each side of the equation.
-6 + -2ln + 6 + lnx = 0 + 6

Reorder the terms:
-6 + 6 + -2ln + lnx = 0 + 6

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

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

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.