ln(x)-ln(x+1)=ln(x+3)-ln(x-5)

Solution for ln(x)-ln(x+1)=ln(x+3)-ln(x-5) equation:

Simplifying
ln(x) + -1ln(x + 1) = ln(x + 3) + -1ln(x + -5)

Multiply ln * x
lnx + -1ln(x + 1) = ln(x + 3) + -1ln(x + -5)

Reorder the terms:
lnx + -1ln(1 + x) = ln(x + 3) + -1ln(x + -5)
lnx + (1 * -1ln + x * -1ln) = ln(x + 3) + -1ln(x + -5)
lnx + (-1ln + -1lnx) = ln(x + 3) + -1ln(x + -5)

Reorder the terms:
-1ln + lnx + -1lnx = ln(x + 3) + -1ln(x + -5)

Combine like terms: lnx + -1lnx = 0
-1ln + 0 = ln(x + 3) + -1ln(x + -5)
-1ln = ln(x + 3) + -1ln(x + -5)

Reorder the terms:
-1ln = ln(3 + x) + -1ln(x + -5)
-1ln = (3 * ln + x * ln) + -1ln(x + -5)
-1ln = (3ln + lnx) + -1ln(x + -5)

Reorder the terms:
-1ln = 3ln + lnx + -1ln(-5 + x)
-1ln = 3ln + lnx + (-5 * -1ln + x * -1ln)
-1ln = 3ln + lnx + (5ln + -1lnx)

Reorder the terms:
-1ln = 3ln + 5ln + lnx + -1lnx

Combine like terms: 3ln + 5ln = 8ln
-1ln = 8ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln = 8ln + 0
-1ln = 8ln

Solving
-1ln = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-1ln + -8ln = 8ln + -8ln

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

Combine like terms: 8ln + -8ln = 0
-9ln = 0

Divide each side by '-9'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.