ln(x+5)+ln(x-1)=2

Solution for ln(x+5)+ln(x-1)=2 equation:

Simplifying
ln(x + 5) + ln(x + -1) = 2

Reorder the terms:
ln(5 + x) + ln(x + -1) = 2
(5 * ln + x * ln) + ln(x + -1) = 2
(5ln + lnx) + ln(x + -1) = 2

Reorder the terms:
5ln + lnx + ln(-1 + x) = 2
5ln + lnx + (-1 * ln + x * ln) = 2
5ln + lnx + (-1ln + lnx) = 2

Reorder the terms:
5ln + -1ln + lnx + lnx = 2

Combine like terms: 5ln + -1ln = 4ln
4ln + lnx + lnx = 2

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

Solving
4ln + 2lnx = 2

Solving for variable 'l'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2ln + lnx) = 0

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

Simplifying
-1 + 2ln + lnx = 0

Solving
-1 + 2ln + lnx = 0

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

Add '1' to each side of the equation.
-1 + 2ln + 1 + lnx = 0 + 1

Reorder the terms:
-1 + 1 + 2ln + lnx = 0 + 1

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

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

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.