ln(x-7)-ln(x+2)=ln(x-4)-ln(x+2)

Solution for ln(x-7)-ln(x+2)=ln(x-4)-ln(x+2) equation:

Simplifying
ln(x + -7) + -1ln(x + 2) = ln(x + -4) + -1ln(x + 2)

Reorder the terms:
ln(-7 + x) + -1ln(x + 2) = ln(x + -4) + -1ln(x + 2)
(-7 * ln + x * ln) + -1ln(x + 2) = ln(x + -4) + -1ln(x + 2)
(-7ln + lnx) + -1ln(x + 2) = ln(x + -4) + -1ln(x + 2)

Reorder the terms:
-7ln + lnx + -1ln(2 + x) = ln(x + -4) + -1ln(x + 2)
-7ln + lnx + (2 * -1ln + x * -1ln) = ln(x + -4) + -1ln(x + 2)
-7ln + lnx + (-2ln + -1lnx) = ln(x + -4) + -1ln(x + 2)

Reorder the terms:
-7ln + -2ln + lnx + -1lnx = ln(x + -4) + -1ln(x + 2)

Combine like terms: -7ln + -2ln = -9ln
-9ln + lnx + -1lnx = ln(x + -4) + -1ln(x + 2)

Combine like terms: lnx + -1lnx = 0
-9ln + 0 = ln(x + -4) + -1ln(x + 2)
-9ln = ln(x + -4) + -1ln(x + 2)

Reorder the terms:
-9ln = ln(-4 + x) + -1ln(x + 2)
-9ln = (-4 * ln + x * ln) + -1ln(x + 2)
-9ln = (-4ln + lnx) + -1ln(x + 2)

Reorder the terms:
-9ln = -4ln + lnx + -1ln(2 + x)
-9ln = -4ln + lnx + (2 * -1ln + x * -1ln)
-9ln = -4ln + lnx + (-2ln + -1lnx)

Reorder the terms:
-9ln = -4ln + -2ln + lnx + -1lnx

Combine like terms: -4ln + -2ln = -6ln
-9ln = -6ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-9ln = -6ln + 0
-9ln = -6ln

Solving
-9ln = -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.
-9ln + 6ln = -6ln + 6ln

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

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

Divide each side by '-3'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.