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

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

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

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

Remove parenthesis around (-2 + x)
-2 + x + ln(x + 1) = ln(x + -3)

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

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

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

Add '-1lnx' to each side of the equation.
-2 + 1ln + lnx + -1lnx + x = -3ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-2 + 1ln + 0 + x = -3ln + lnx + -1lnx
-2 + 1ln + x = -3ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-2 + 1ln + x = -3ln + 0
-2 + 1ln + x = -3ln

Solving
-2 + 1ln + x = -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.
-2 + 1ln + 3ln + x = -3ln + 3ln

Combine like terms: 1ln + 3ln = 4ln
-2 + 4ln + x = -3ln + 3ln

Combine like terms: -3ln + 3ln = 0
-2 + 4ln + x = 0

Add '2' to each side of the equation.
-2 + 4ln + 2 + x = 0 + 2

Reorder the terms:
-2 + 2 + 4ln + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4ln + x = 0 + 2
4ln + x = 0 + 2

Combine like terms: 0 + 2 = 2
4ln + x = 2

Add '-1x' to each side of the equation.
4ln + x + -1x = 2 + -1x

Combine like terms: x + -1x = 0
4ln + 0 = 2 + -1x
4ln = 2 + -1x

Divide each side by '4n'.
l = 0.5n-1 + -0.25n-1x

Simplifying
l = 0.5n-1 + -0.25n-1x