ln(x+10)-ln(x-6)=l

Solution for ln(x+10)-ln(x-6)=l equation:

Simplifying
ln(x + 10) + -1ln(x + -6) = l

Reorder the terms:
ln(10 + x) + -1ln(x + -6) = l
(10 * ln + x * ln) + -1ln(x + -6) = l
(10ln + lnx) + -1ln(x + -6) = l

Reorder the terms:
10ln + lnx + -1ln(-6 + x) = l
10ln + lnx + (-6 * -1ln + x * -1ln) = l
10ln + lnx + (6ln + -1lnx) = l

Reorder the terms:
10ln + 6ln + lnx + -1lnx = l

Combine like terms: 10ln + 6ln = 16ln
16ln + lnx + -1lnx = l

Combine like terms: lnx + -1lnx = 0
16ln + 0 = l
16ln = l

Solving
16ln = l

Solving for variable 'l'.

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

Add '-1l' to each side of the equation.
-1l + 16ln = l + -1l

Combine like terms: l + -1l = 0
-1l + 16ln = 0

Factor out the Greatest Common Factor (GCF), 'l'.
l(-1 + 16n) = 0

Subproblem 1
Set the factor 'l' equal to zero and attempt to solve:

Simplifying
l = 0

Solving
l = 0

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

Simplifying
l = 0
Subproblem 2
Set the factor '(-1 + 16n)' equal to zero and attempt to solve:

Simplifying
-1 + 16n = 0

Solving
-1 + 16n = 0

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

Add '1' to each side of the equation.
-1 + 1 + 16n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 16n = 0 + 1
16n = 0 + 1

Combine like terms: 0 + 1 = 1
16n = 1

Add '-16n' to each side of the equation.
16n + -16n = 1 + -16n

Combine like terms: 16n + -16n = 0
0 = 1 + -16n

Simplifying
0 = 1 + -16n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
l = {0}