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

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

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

Reorder the terms:
nL(-1 + x) + ln(x + -1) + -1ln(x + 2) = ln(3)
(-1 * nL + x * nL) + ln(x + -1) + -1ln(x + 2) = ln(3)
(-1nL + nxL) + ln(x + -1) + -1ln(x + 2) = ln(3)

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

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

Reorder the terms:
-1ln + -2ln + lnx + -1lnx + -1nL + nxL = ln(3)

Combine like terms: -1ln + -2ln = -3ln
-3ln + lnx + -1lnx + -1nL + nxL = ln(3)

Combine like terms: lnx + -1lnx = 0
-3ln + 0 + -1nL + nxL = ln(3)
-3ln + -1nL + nxL = ln(3)

Reorder the terms for easier multiplication:
-3ln + -1nL + nxL = 3ln

Solving
-3ln + -1nL + nxL = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-3ln + -1nL + -3ln + nxL = 3ln + -3ln

Reorder the terms:
-3ln + -3ln + -1nL + nxL = 3ln + -3ln

Combine like terms: -3ln + -3ln = -6ln
-6ln + -1nL + nxL = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-6ln + -1nL + nxL = 0

Add 'nL' to each side of the equation.
-6ln + -1nL + nL + nxL = 0 + nL

Combine like terms: -1nL + nL = 0
-6ln + 0 + nxL = 0 + nL
-6ln + nxL = 0 + nL
Remove the zero:
-6ln + nxL = nL

Add '-1nxL' to each side of the equation.
-6ln + nxL + -1nxL = nL + -1nxL

Combine like terms: nxL + -1nxL = 0
-6ln + 0 = nL + -1nxL
-6ln = nL + -1nxL

Divide each side by '-6n'.
l = -0.1666666667L + 0.1666666667xL

Simplifying
l = -0.1666666667L + 0.1666666667xL