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

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

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

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

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

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

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

Combine like terms: 1ln + -1ln = 0
5ln + lnx = 0 + lnx + -1lnx
5ln + lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
5ln + lnx = 0

Solving
5ln + lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Add '-1x' to each side of the equation.
x + -1x = -5 + -1x

Combine like terms: x + -1x = 0
0 = -5 + -1x

Simplifying
0 = -5 + -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.