ln(-3y+4)-ln(y+5)=ln(-9y-10)

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Solution for ln(-3y+4)-ln(y+5)=ln(-9y-10) equation:


Simplifying
ln(-3y + 4) + -1ln(y + 5) = ln(-9y + -10)

Reorder the terms:
ln(4 + -3y) + -1ln(y + 5) = ln(-9y + -10)
(4 * ln + -3y * ln) + -1ln(y + 5) = ln(-9y + -10)
(4ln + -3lny) + -1ln(y + 5) = ln(-9y + -10)

Reorder the terms:
4ln + -3lny + -1ln(5 + y) = ln(-9y + -10)
4ln + -3lny + (5 * -1ln + y * -1ln) = ln(-9y + -10)
4ln + -3lny + (-5ln + -1lny) = ln(-9y + -10)

Reorder the terms:
4ln + -5ln + -3lny + -1lny = ln(-9y + -10)

Combine like terms: 4ln + -5ln = -1ln
-1ln + -3lny + -1lny = ln(-9y + -10)

Combine like terms: -3lny + -1lny = -4lny
-1ln + -4lny = ln(-9y + -10)

Reorder the terms:
-1ln + -4lny = ln(-10 + -9y)
-1ln + -4lny = (-10 * ln + -9y * ln)
-1ln + -4lny = (-10ln + -9lny)

Solving
-1ln + -4lny = -10ln + -9lny

Solving for variable 'l'.

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

Add '10ln' to each side of the equation.
-1ln + 10ln + -4lny = -10ln + 10ln + -9lny

Combine like terms: -1ln + 10ln = 9ln
9ln + -4lny = -10ln + 10ln + -9lny

Combine like terms: -10ln + 10ln = 0
9ln + -4lny = 0 + -9lny
9ln + -4lny = -9lny

Add '9lny' to each side of the equation.
9ln + -4lny + 9lny = -9lny + 9lny

Combine like terms: -4lny + 9lny = 5lny
9ln + 5lny = -9lny + 9lny

Combine like terms: -9lny + 9lny = 0
9ln + 5lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(9 + 5y) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(9 + 5y)' equal to zero and attempt to solve: Simplifying 9 + 5y = 0 Solving 9 + 5y = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5y = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5y = 0 + -9 5y = 0 + -9 Combine like terms: 0 + -9 = -9 5y = -9 Add '-5y' to each side of the equation. 5y + -5y = -9 + -5y Combine like terms: 5y + -5y = 0 0 = -9 + -5y Simplifying 0 = -9 + -5y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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