ln(x-10)-ln(x+3)=ln(x-3)-ln(x+7)

Solution for ln(x-10)-ln(x+3)=ln(x-3)-ln(x+7) equation:

Simplifying
ln(x + -10) + -1ln(x + 3) = ln(x + -3) + -1ln(x + 7)

Reorder the terms:
ln(-10 + x) + -1ln(x + 3) = ln(x + -3) + -1ln(x + 7)
(-10 * ln + x * ln) + -1ln(x + 3) = ln(x + -3) + -1ln(x + 7)
(-10ln + lnx) + -1ln(x + 3) = ln(x + -3) + -1ln(x + 7)

Reorder the terms:
-10ln + lnx + -1ln(3 + x) = ln(x + -3) + -1ln(x + 7)
-10ln + lnx + (3 * -1ln + x * -1ln) = ln(x + -3) + -1ln(x + 7)
-10ln + lnx + (-3ln + -1lnx) = ln(x + -3) + -1ln(x + 7)

Reorder the terms:
-10ln + -3ln + lnx + -1lnx = ln(x + -3) + -1ln(x + 7)

Combine like terms: -10ln + -3ln = -13ln
-13ln + lnx + -1lnx = ln(x + -3) + -1ln(x + 7)

Combine like terms: lnx + -1lnx = 0
-13ln + 0 = ln(x + -3) + -1ln(x + 7)
-13ln = ln(x + -3) + -1ln(x + 7)

Reorder the terms:
-13ln = ln(-3 + x) + -1ln(x + 7)
-13ln = (-3 * ln + x * ln) + -1ln(x + 7)
-13ln = (-3ln + lnx) + -1ln(x + 7)

Reorder the terms:
-13ln = -3ln + lnx + -1ln(7 + x)
-13ln = -3ln + lnx + (7 * -1ln + x * -1ln)
-13ln = -3ln + lnx + (-7ln + -1lnx)

Reorder the terms:
-13ln = -3ln + -7ln + lnx + -1lnx

Combine like terms: -3ln + -7ln = -10ln
-13ln = -10ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-13ln = -10ln + 0
-13ln = -10ln

Solving
-13ln = -10ln

Solving for variable 'l'.

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

Add '10ln' to each side of the equation.
-13ln + 10ln = -10ln + 10ln

Combine like terms: -13ln + 10ln = -3ln
-3ln = -10ln + 10ln

Combine like terms: -10ln + 10ln = 0
-3ln = 0

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

Simplifying
ln = 0

The solution to this equation could not be determined.