ln(x+3)+2=12-ln(x-2)

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Solution for ln(x+3)+2=12-ln(x-2) equation: 


Simplifying
ln(x + 3) + 2 = 12 + -1ln(x + -2)

Reorder the terms:
ln(3 + x) + 2 = 12 + -1ln(x + -2)
(3 * ln + x * ln) + 2 = 12 + -1ln(x + -2)
(3ln + lnx) + 2 = 12 + -1ln(x + -2)

Reorder the terms:
2 + 3ln + lnx = 12 + -1ln(x + -2)

Reorder the terms:
2 + 3ln + lnx = 12 + -1ln(-2 + x)
2 + 3ln + lnx = 12 + (-2 * -1ln + x * -1ln)
2 + 3ln + lnx = 12 + (2ln + -1lnx)

Solving
2 + 3ln + lnx = 12 + 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.
2 + 3ln + -2ln + lnx = 12 + 2ln + -2ln + -1lnx

Combine like terms: 3ln + -2ln = 1ln
2 + 1ln + lnx = 12 + 2ln + -2ln + -1lnx

Combine like terms: 2ln + -2ln = 0
2 + 1ln + lnx = 12 + 0 + -1lnx
2 + 1ln + lnx = 12 + -1lnx

Add 'lnx' to each side of the equation.
2 + 1ln + lnx + lnx = 12 + -1lnx + lnx

Combine like terms: lnx + lnx = 2lnx
2 + 1ln + 2lnx = 12 + -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
2 + 1ln + 2lnx = 12 + 0
2 + 1ln + 2lnx = 12

Add '-2' to each side of the equation.
2 + 1ln + -2 + 2lnx = 12 + -2

Reorder the terms:
2 + -2 + 1ln + 2lnx = 12 + -2

Combine like terms: 2 + -2 = 0
0 + 1ln + 2lnx = 12 + -2
1ln + 2lnx = 12 + -2

Combine like terms: 12 + -2 = 10
1ln + 2lnx = 10

Reorder the terms:
-10 + 1ln + 2lnx = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 1ln + 2lnx = 0

The solution to this equation could not be determined.

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