ln(x+6)+ln(x+2)=ln(5)

Solution for ln(x+6)+ln(x+2)=ln(5) equation:

Simplifying
ln(x + 6) + ln(x + 2) = ln(5)

Reorder the terms:
ln(6 + x) + ln(x + 2) = ln(5)
(6 * ln + x * ln) + ln(x + 2) = ln(5)
(6ln + lnx) + ln(x + 2) = ln(5)

Reorder the terms:
6ln + lnx + ln(2 + x) = ln(5)
6ln + lnx + (2 * ln + x * ln) = ln(5)
6ln + lnx + (2ln + lnx) = ln(5)

Reorder the terms:
6ln + 2ln + lnx + lnx = ln(5)

Combine like terms: 6ln + 2ln = 8ln
8ln + lnx + lnx = ln(5)

Combine like terms: lnx + lnx = 2lnx
8ln + 2lnx = ln(5)

Reorder the terms for easier multiplication:
8ln + 2lnx = 5ln

Solving
8ln + 2lnx = 5ln

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
8ln + -5ln + 2lnx = 5ln + -5ln

Combine like terms: 8ln + -5ln = 3ln
3ln + 2lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
3ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + 2x) = 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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Add '-2x' to each side of the equation.
2x + -2x = -3 + -2x

Combine like terms: 2x + -2x = 0
0 = -3 + -2x

Simplifying
0 = -3 + -2x

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.