ln(-5n)=ln(4-3n)

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Solution for ln(-5n)=ln(4-3n) equation:


Simplifying
ln(-5n) = ln(4 + -3n)

Remove parenthesis around (-5n)
ln * -5n = ln(4 + -3n)

Reorder the terms for easier multiplication:
-5ln * n = ln(4 + -3n)

Multiply ln * n
-5ln2 = ln(4 + -3n)
-5ln2 = (4 * ln + -3n * ln)
-5ln2 = (4ln + -3ln2)

Solving
-5ln2 = 4ln + -3ln2

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-4ln + -5ln2 = 4ln + -4ln + -3ln2

Combine like terms: 4ln + -4ln = 0
-4ln + -5ln2 = 0 + -3ln2
-4ln + -5ln2 = -3ln2

Add '3ln2' to each side of the equation.
-4ln + -5ln2 + 3ln2 = -3ln2 + 3ln2

Combine like terms: -5ln2 + 3ln2 = -2ln2
-4ln + -2ln2 = -3ln2 + 3ln2

Combine like terms: -3ln2 + 3ln2 = 0
-4ln + -2ln2 = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(2 + n) = 0

Ignore the factor -2.

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 '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Add '-1n' to each side of the equation. n + -1n = -2 + -1n Combine like terms: n + -1n = 0 0 = -2 + -1n Simplifying 0 = -2 + -1n 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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