Ln(4-y)-ln(y)=3x+ln(8)

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Solution for Ln(4-y)-ln(y)=3x+ln(8) equation: 


Simplifying
Ln(4 + -1y) + -1ln(y) = 3x + ln(8)
(4 * nL + -1y * nL) + -1ln(y) = 3x + ln(8)
(4nL + -1nyL) + -1ln(y) = 3x + ln(8)

Multiply ln * y
4nL + -1nyL + -1lny = 3x + ln(8)

Reorder the terms:
-1lny + 4nL + -1nyL = 3x + ln(8)

Reorder the terms for easier multiplication:
-1lny + 4nL + -1nyL = 3x + 8ln

Reorder the terms:
-1lny + 4nL + -1nyL = 8ln + 3x

Solving
-1lny + 4nL + -1nyL = 8ln + 3x

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
-1lny + 4nL + -8ln + -1nyL = 8ln + -8ln + 3x

Reorder the terms:
-8ln + -1lny + 4nL + -1nyL = 8ln + -8ln + 3x

Combine like terms: 8ln + -8ln = 0
-8ln + -1lny + 4nL + -1nyL = 0 + 3x
-8ln + -1lny + 4nL + -1nyL = 3x

Add '-4nL' to each side of the equation.
-8ln + -1lny + 4nL + -4nL + -1nyL = -4nL + 3x

Combine like terms: 4nL + -4nL = 0
-8ln + -1lny + 0 + -1nyL = -4nL + 3x
-8ln + -1lny + -1nyL = -4nL + 3x

Add 'nyL' to each side of the equation.
-8ln + -1lny + -1nyL + nyL = -4nL + nyL + 3x

Combine like terms: -1nyL + nyL = 0
-8ln + -1lny + 0 = -4nL + nyL + 3x
-8ln + -1lny = -4nL + nyL + 3x

Reorder the terms:
-8ln + -1lny + 4nL + -1nyL + -3x = -4nL + 4nL + nyL + -1nyL + 3x + -3x

Combine like terms: -4nL + 4nL = 0
-8ln + -1lny + 4nL + -1nyL + -3x = 0 + nyL + -1nyL + 3x + -3x
-8ln + -1lny + 4nL + -1nyL + -3x = nyL + -1nyL + 3x + -3x

Combine like terms: nyL + -1nyL = 0
-8ln + -1lny + 4nL + -1nyL + -3x = 0 + 3x + -3x
-8ln + -1lny + 4nL + -1nyL + -3x = 3x + -3x

Combine like terms: 3x + -3x = 0
-8ln + -1lny + 4nL + -1nyL + -3x = 0

The solution to this equation could not be determined.

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