ln(x-2)-ln(x+3)=ln(x-1)-ln(x-7)

Solution for ln(x-2)-ln(x+3)=ln(x-1)-ln(x-7) equation:

Simplifying
ln(x + -2) + -1ln(x + 3) = ln(x + -1) + -1ln(x + -7)

Reorder the terms:
ln(-2 + x) + -1ln(x + 3) = ln(x + -1) + -1ln(x + -7)
(-2 * ln + x * ln) + -1ln(x + 3) = ln(x + -1) + -1ln(x + -7)
(-2ln + lnx) + -1ln(x + 3) = ln(x + -1) + -1ln(x + -7)

Reorder the terms:
-2ln + lnx + -1ln(3 + x) = ln(x + -1) + -1ln(x + -7)
-2ln + lnx + (3 * -1ln + x * -1ln) = ln(x + -1) + -1ln(x + -7)
-2ln + lnx + (-3ln + -1lnx) = ln(x + -1) + -1ln(x + -7)

Reorder the terms:
-2ln + -3ln + lnx + -1lnx = ln(x + -1) + -1ln(x + -7)

Combine like terms: -2ln + -3ln = -5ln
-5ln + lnx + -1lnx = ln(x + -1) + -1ln(x + -7)

Combine like terms: lnx + -1lnx = 0
-5ln + 0 = ln(x + -1) + -1ln(x + -7)
-5ln = ln(x + -1) + -1ln(x + -7)

Reorder the terms:
-5ln = ln(-1 + x) + -1ln(x + -7)
-5ln = (-1 * ln + x * ln) + -1ln(x + -7)
-5ln = (-1ln + lnx) + -1ln(x + -7)

Reorder the terms:
-5ln = -1ln + lnx + -1ln(-7 + x)
-5ln = -1ln + lnx + (-7 * -1ln + x * -1ln)
-5ln = -1ln + lnx + (7ln + -1lnx)

Reorder the terms:
-5ln = -1ln + 7ln + lnx + -1lnx

Combine like terms: -1ln + 7ln = 6ln
-5ln = 6ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-5ln = 6ln + 0
-5ln = 6ln

Solving
-5ln = 6ln

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
-5ln + -6ln = 6ln + -6ln

Combine like terms: -5ln + -6ln = -11ln
-11ln = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-11ln = 0

Divide each side by '-11'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.