ln(x+4)=ln(x+1)+ln(x+3)-ln(x+2)

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Solution for ln(x+4)=ln(x+1)+ln(x+3)-ln(x+2) equation: 


Simplifying
ln(x + 4) = ln(x + 1) + ln(x + 3) + -1ln(x + 2)

Reorder the terms:
ln(4 + x) = ln(x + 1) + ln(x + 3) + -1ln(x + 2)
(4 * ln + x * ln) = ln(x + 1) + ln(x + 3) + -1ln(x + 2)
(4ln + lnx) = ln(x + 1) + ln(x + 3) + -1ln(x + 2)

Reorder the terms:
4ln + lnx = ln(1 + x) + ln(x + 3) + -1ln(x + 2)
4ln + lnx = (1 * ln + x * ln) + ln(x + 3) + -1ln(x + 2)
4ln + lnx = (1ln + lnx) + ln(x + 3) + -1ln(x + 2)

Reorder the terms:
4ln + lnx = 1ln + lnx + ln(3 + x) + -1ln(x + 2)
4ln + lnx = 1ln + lnx + (3 * ln + x * ln) + -1ln(x + 2)
4ln + lnx = 1ln + lnx + (3ln + lnx) + -1ln(x + 2)

Reorder the terms:
4ln + lnx = 1ln + lnx + 3ln + lnx + -1ln(2 + x)
4ln + lnx = 1ln + lnx + 3ln + lnx + (2 * -1ln + x * -1ln)
4ln + lnx = 1ln + lnx + 3ln + lnx + (-2ln + -1lnx)

Reorder the terms:
4ln + lnx = 1ln + 3ln + -2ln + lnx + lnx + -1lnx

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

Combine like terms: 4ln + -2ln = 2ln
4ln + lnx = 2ln + lnx + lnx + -1lnx

Combine like terms: lnx + lnx = 2lnx
4ln + lnx = 2ln + 2lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
4ln + lnx = 2ln + 1lnx

Solving
4ln + lnx = 2ln + 1lnx

Solving for variable 'l'.

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

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

Combine like terms: 4ln + -2ln = 2ln
2ln + lnx = 2ln + -2ln + 1lnx

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

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

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

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

Divide each side by '2'.
ln = 0

Simplifying
ln = 0

The solution to this equation could not be determined.

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