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

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:
ln(-5 + x) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)
(-5 * ln + x * ln) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)
(-5ln + lnx) + -1ln(x + 4) = ln(x + -1) + -1ln(x + 2)

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

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

Combine like terms: -5ln + -4ln = -9ln
-9ln + lnx + -1lnx = ln(x + -1) + -1ln(x + 2)

Combine like terms: lnx + -1lnx = 0
-9ln + 0 = ln(x + -1) + -1ln(x + 2)
-9ln = ln(x + -1) + -1ln(x + 2)

Reorder the terms:
-9ln = ln(-1 + x) + -1ln(x + 2)
-9ln = (-1 * ln + x * ln) + -1ln(x + 2)
-9ln = (-1ln + lnx) + -1ln(x + 2)

Reorder the terms:
-9ln = -1ln + lnx + -1ln(2 + x)
-9ln = -1ln + lnx + (2 * -1ln + x * -1ln)
-9ln = -1ln + lnx + (-2ln + -1lnx)

Reorder the terms:
-9ln = -1ln + -2ln + lnx + -1lnx

Combine like terms: -1ln + -2ln = -3ln
-9ln = -3ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-9ln = -3ln + 0
-9ln = -3ln

Solving
-9ln = -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.
-9ln + 3ln = -3ln + 3ln

Combine like terms: -9ln + 3ln = -6ln
-6ln = -3ln + 3ln

Combine like terms: -3ln + 3ln = 0
-6ln = 0

Divide each side by '-6'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.