Ln(x+5)-ln(x+4)=ln(x-1)-ln(x+2)

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Solution for Ln(x+5)-ln(x+4)=ln(x-1)-ln(x+2) equation: 


Simplifying
Ln(x + 5) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)

Reorder the terms:
nL(5 + x) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)
(5 * nL + x * nL) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)
(5nL + nxL) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)

Reorder the terms:
5nL + nxL + -1ln(4 + x) = ln(x + -1) + -1ln(x + 2)
5nL + nxL + (4 * -1ln + x * -1ln) = ln(x + -1) + -1ln(x + 2)
5nL + nxL + (-4ln + -1lnx) = ln(x + -1) + -1ln(x + 2)

Reorder the terms:
-4ln + -1lnx + 5nL + nxL = ln(x + -1) + -1ln(x + 2)

Reorder the terms:
-4ln + -1lnx + 5nL + nxL = ln(-1 + x) + -1ln(x + 2)
-4ln + -1lnx + 5nL + nxL = (-1 * ln + x * ln) + -1ln(x + 2)
-4ln + -1lnx + 5nL + nxL = (-1ln + lnx) + -1ln(x + 2)

Reorder the terms:
-4ln + -1lnx + 5nL + nxL = -1ln + lnx + -1ln(2 + x)
-4ln + -1lnx + 5nL + nxL = -1ln + lnx + (2 * -1ln + x * -1ln)
-4ln + -1lnx + 5nL + nxL = -1ln + lnx + (-2ln + -1lnx)

Reorder the terms:
-4ln + -1lnx + 5nL + nxL = -1ln + -2ln + lnx + -1lnx

Combine like terms: -1ln + -2ln = -3ln
-4ln + -1lnx + 5nL + nxL = -3ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-4ln + -1lnx + 5nL + nxL = -3ln + 0
-4ln + -1lnx + 5nL + nxL = -3ln

Solving
-4ln + -1lnx + 5nL + nxL = -3ln

Solving for variable 'l'.

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

Add '3ln' to each side of the equation.
-4ln + -1lnx + 5nL + 3ln + nxL = -3ln + 3ln

Reorder the terms:
-4ln + 3ln + -1lnx + 5nL + nxL = -3ln + 3ln

Combine like terms: -4ln + 3ln = -1ln
-1ln + -1lnx + 5nL + nxL = -3ln + 3ln

Combine like terms: -3ln + 3ln = 0
-1ln + -1lnx + 5nL + nxL = 0

Add '-5nL' to each side of the equation.
-1ln + -1lnx + 5nL + -5nL + nxL = 0 + -5nL

Combine like terms: 5nL + -5nL = 0
-1ln + -1lnx + 0 + nxL = 0 + -5nL
-1ln + -1lnx + nxL = 0 + -5nL
Remove the zero:
-1ln + -1lnx + nxL = -5nL

Add '-1nxL' to each side of the equation.
-1ln + -1lnx + nxL + -1nxL = -5nL + -1nxL

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1l + -1lx + 5L + xL) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-1l + -1lx + 5L + xL)' equal to zero and attempt to solve:

Simplifying
-1l + -1lx + 5L + xL = 0

Reorder the terms:
5L + -1l + -1lx + xL = 0

Solving
5L + -1l + -1lx + xL = 0

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

Add '-5L' to each side of the equation.
5L + -1l + -1lx + -5L + xL = 0 + -5L

Reorder the terms:
5L + -5L + -1l + -1lx + xL = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + -1l + -1lx + xL = 0 + -5L
-1l + -1lx + xL = 0 + -5L
Remove the zero:
-1l + -1lx + xL = -5L

Add '-1xL' to each side of the equation.
-1l + -1lx + xL + -1xL = -5L + -1xL

Combine like terms: xL + -1xL = 0
-1l + -1lx + 0 = -5L + -1xL
-1l + -1lx = -5L + -1xL

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.

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