ln(x-3)-ln(x+8)=(x-2)-ln(x+11)

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Solution for ln(x-3)-ln(x+8)=(x-2)-ln(x+11) equation: 


Simplifying
ln(x + -3) + -1ln(x + 8) = (x + -2) + -1ln(x + 11)

Reorder the terms:
ln(-3 + x) + -1ln(x + 8) = (x + -2) + -1ln(x + 11)
(-3 * ln + x * ln) + -1ln(x + 8) = (x + -2) + -1ln(x + 11)
(-3ln + lnx) + -1ln(x + 8) = (x + -2) + -1ln(x + 11)

Reorder the terms:
-3ln + lnx + -1ln(8 + x) = (x + -2) + -1ln(x + 11)
-3ln + lnx + (8 * -1ln + x * -1ln) = (x + -2) + -1ln(x + 11)
-3ln + lnx + (-8ln + -1lnx) = (x + -2) + -1ln(x + 11)

Reorder the terms:
-3ln + -8ln + lnx + -1lnx = (x + -2) + -1ln(x + 11)

Combine like terms: -3ln + -8ln = -11ln
-11ln + lnx + -1lnx = (x + -2) + -1ln(x + 11)

Combine like terms: lnx + -1lnx = 0
-11ln + 0 = (x + -2) + -1ln(x + 11)
-11ln = (x + -2) + -1ln(x + 11)

Reorder the terms:
-11ln = (-2 + x) + -1ln(x + 11)

Remove parenthesis around (-2 + x)
-11ln = -2 + x + -1ln(x + 11)

Reorder the terms:
-11ln = -2 + x + -1ln(11 + x)
-11ln = -2 + x + (11 * -1ln + x * -1ln)
-11ln = -2 + x + (-11ln + -1lnx)

Reorder the terms:
-11ln = -2 + -11ln + -1lnx + x

Add '11ln' to each side of the equation.
-11ln + 11ln = -2 + -11ln + -1lnx + 11ln + x

Combine like terms: -11ln + 11ln = 0
0 = -2 + -11ln + -1lnx + 11ln + x

Reorder the terms:
0 = -2 + -11ln + 11ln + -1lnx + x

Combine like terms: -11ln + 11ln = 0
0 = -2 + 0 + -1lnx + x
0 = -2 + -1lnx + x

Solving
0 = -2 + -1lnx + x

Solving for variable 'l'.

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

Add 'lnx' to each side of the equation.
0 + lnx = -2 + -1lnx + lnx + x
Remove the zero:
lnx = -2 + -1lnx + lnx + x

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

Divide each side by 'nx'.
l = -2n-1x-1 + n-1

Simplifying
l = -2n-1x-1 + n-1

Reorder the terms:
l = n-1 + -2n-1x-1

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