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

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

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

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

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

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

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

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

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

Solving
3 + -2ln = 1ln

Solving for variable 'l'.

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

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

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

Combine like terms: 1ln + -1ln = 0
3 + -3ln = 0

Add '-3' to each side of the equation.
3 + -3 + -3ln = 0 + -3

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

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

Divide each side by '-3n'.
l = n-1

Simplifying
l = n-1