Ln(x-2)-ln(x+5)=ln(x-1)-ln(x+11)

Solution for Ln(x-2)-ln(x+5)=ln(x-1)-ln(x+11) equation:

Simplifying
Ln(x + -2) + -1ln(x + 5) = ln(x + -1) + -1ln(x + 11)

Reorder the terms:
nL(-2 + x) + -1ln(x + 5) = ln(x + -1) + -1ln(x + 11)
(-2 * nL + x * nL) + -1ln(x + 5) = ln(x + -1) + -1ln(x + 11)
(-2nL + nxL) + -1ln(x + 5) = ln(x + -1) + -1ln(x + 11)

Reorder the terms:
-2nL + nxL + -1ln(5 + x) = ln(x + -1) + -1ln(x + 11)
-2nL + nxL + (5 * -1ln + x * -1ln) = ln(x + -1) + -1ln(x + 11)
-2nL + nxL + (-5ln + -1lnx) = ln(x + -1) + -1ln(x + 11)

Reorder the terms:
-5ln + -1lnx + -2nL + nxL = ln(x + -1) + -1ln(x + 11)

Reorder the terms:
-5ln + -1lnx + -2nL + nxL = ln(-1 + x) + -1ln(x + 11)
-5ln + -1lnx + -2nL + nxL = (-1 * ln + x * ln) + -1ln(x + 11)
-5ln + -1lnx + -2nL + nxL = (-1ln + lnx) + -1ln(x + 11)

Reorder the terms:
-5ln + -1lnx + -2nL + nxL = -1ln + lnx + -1ln(11 + x)
-5ln + -1lnx + -2nL + nxL = -1ln + lnx + (11 * -1ln + x * -1ln)
-5ln + -1lnx + -2nL + nxL = -1ln + lnx + (-11ln + -1lnx)

Reorder the terms:
-5ln + -1lnx + -2nL + nxL = -1ln + -11ln + lnx + -1lnx

Combine like terms: -1ln + -11ln = -12ln
-5ln + -1lnx + -2nL + nxL = -12ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-5ln + -1lnx + -2nL + nxL = -12ln + 0
-5ln + -1lnx + -2nL + nxL = -12ln

Solving
-5ln + -1lnx + -2nL + nxL = -12ln

Solving for variable 'l'.

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

Add '12ln' to each side of the equation.
-5ln + -1lnx + -2nL + 12ln + nxL = -12ln + 12ln

Reorder the terms:
-5ln + 12ln + -1lnx + -2nL + nxL = -12ln + 12ln

Combine like terms: -5ln + 12ln = 7ln
7ln + -1lnx + -2nL + nxL = -12ln + 12ln

Combine like terms: -12ln + 12ln = 0
7ln + -1lnx + -2nL + nxL = 0

Add '2nL' to each side of the equation.
7ln + -1lnx + -2nL + 2nL + nxL = 0 + 2nL

Combine like terms: -2nL + 2nL = 0
7ln + -1lnx + 0 + nxL = 0 + 2nL
7ln + -1lnx + nxL = 0 + 2nL
Remove the zero:
7ln + -1lnx + nxL = 2nL

Add '-1nxL' to each side of the equation.
7ln + -1lnx + nxL + -1nxL = 2nL + -1nxL

Combine like terms: nxL + -1nxL = 0
7ln + -1lnx + 0 = 2nL + -1nxL
7ln + -1lnx = 2nL + -1nxL

Reorder the terms:
7ln + -1lnx + -2nL + nxL = 2nL + -2nL + -1nxL + nxL

Combine like terms: 2nL + -2nL = 0
7ln + -1lnx + -2nL + nxL = 0 + -1nxL + nxL
7ln + -1lnx + -2nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
7ln + -1lnx + -2nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(7l + -1lx + -2L + 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 '(7l + -1lx + -2L + xL)' equal to zero and attempt to solve:

Simplifying
7l + -1lx + -2L + xL = 0

Reorder the terms:
-2L + 7l + -1lx + xL = 0

Solving
-2L + 7l + -1lx + xL = 0

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

Add '2L' to each side of the equation.
-2L + 7l + -1lx + 2L + xL = 0 + 2L

Reorder the terms:
-2L + 2L + 7l + -1lx + xL = 0 + 2L

Combine like terms: -2L + 2L = 0
0 + 7l + -1lx + xL = 0 + 2L
7l + -1lx + xL = 0 + 2L
Remove the zero:
7l + -1lx + xL = 2L

Add '-1xL' to each side of the equation.
7l + -1lx + xL + -1xL = 2L + -1xL

Combine like terms: xL + -1xL = 0
7l + -1lx + 0 = 2L + -1xL
7l + -1lx = 2L + -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.