ln(x-2)-ln(x+3)=ln(x-1)-ln(x+8)

Solution for ln(x-2)-ln(x+3)=ln(x-1)-ln(x+8) equation:

Simplifying
ln(x + -2) + -1ln(x + 3) = ln(x + -1) + -1ln(x + 8)

Reorder the terms:
ln(-2 + x) + -1ln(x + 3) = ln(x + -1) + -1ln(x + 8)
(-2 * ln + x * ln) + -1ln(x + 3) = ln(x + -1) + -1ln(x + 8)
(-2ln + lnx) + -1ln(x + 3) = ln(x + -1) + -1ln(x + 8)

Reorder the terms:
-2ln + lnx + -1ln(3 + x) = ln(x + -1) + -1ln(x + 8)
-2ln + lnx + (3 * -1ln + x * -1ln) = ln(x + -1) + -1ln(x + 8)
-2ln + lnx + (-3ln + -1lnx) = ln(x + -1) + -1ln(x + 8)

Reorder the terms:
-2ln + -3ln + lnx + -1lnx = ln(x + -1) + -1ln(x + 8)

Combine like terms: -2ln + -3ln = -5ln
-5ln + lnx + -1lnx = ln(x + -1) + -1ln(x + 8)

Combine like terms: lnx + -1lnx = 0
-5ln + 0 = ln(x + -1) + -1ln(x + 8)
-5ln = ln(x + -1) + -1ln(x + 8)

Reorder the terms:
-5ln = ln(-1 + x) + -1ln(x + 8)
-5ln = (-1 * ln + x * ln) + -1ln(x + 8)
-5ln = (-1ln + lnx) + -1ln(x + 8)

Reorder the terms:
-5ln = -1ln + lnx + -1ln(8 + x)
-5ln = -1ln + lnx + (8 * -1ln + x * -1ln)
-5ln = -1ln + lnx + (-8ln + -1lnx)

Reorder the terms:
-5ln = -1ln + -8ln + lnx + -1lnx

Combine like terms: -1ln + -8ln = -9ln
-5ln = -9ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-5ln = -9ln + 0
-5ln = -9ln

Solving
-5ln = -9ln

Solving for variable 'l'.

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

Add '9ln' to each side of the equation.
-5ln + 9ln = -9ln + 9ln

Combine like terms: -5ln + 9ln = 4ln
4ln = -9ln + 9ln

Combine like terms: -9ln + 9ln = 0
4ln = 0

Divide each side by '4'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.