ln(x+8)+ln(x-8)=ln(6)

Solution for ln(x+8)+ln(x-8)=ln(6) equation:

Simplifying
ln(x + 8) + ln(x + -8) = ln(6)

Reorder the terms:
ln(8 + x) + ln(x + -8) = ln(6)
(8 * ln + x * ln) + ln(x + -8) = ln(6)
(8ln + lnx) + ln(x + -8) = ln(6)

Reorder the terms:
8ln + lnx + ln(-8 + x) = ln(6)
8ln + lnx + (-8 * ln + x * ln) = ln(6)
8ln + lnx + (-8ln + lnx) = ln(6)

Reorder the terms:
8ln + -8ln + lnx + lnx = ln(6)

Combine like terms: 8ln + -8ln = 0
0 + lnx + lnx = ln(6)
lnx + lnx = ln(6)

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

Reorder the terms for easier multiplication:
2lnx = 6ln

Solving
2lnx = 6ln

Solving for variable 'l'.

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

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

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

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

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Add '-1x' to each side of the equation.
x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
0 = 3 + -1x

Simplifying
0 = 3 + -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.