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

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


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

Solving
ln + -5n = 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.
ln + -4ln + -5n = 4ln + -4ln + -3ln2

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

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

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

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

Add '5n' to each side of the equation.
-3ln + 3ln2 + -5n + 5n = 0 + 5n

Combine like terms: -5n + 5n = 0
-3ln + 3ln2 + 0 = 0 + 5n
-3ln + 3ln2 = 0 + 5n
Remove the zero:
-3ln + 3ln2 = 5n

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3l + 3ln + -5) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-3l + 3ln + -5)' equal to zero and attempt to solve: Simplifying -3l + 3ln + -5 = 0 Reorder the terms: -5 + -3l + 3ln = 0 Solving -5 + -3l + 3ln = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -3l + 5 + 3ln = 0 + 5 Reorder the terms: -5 + 5 + -3l + 3ln = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3l + 3ln = 0 + 5 -3l + 3ln = 0 + 5 Combine like terms: 0 + 5 = 5 -3l + 3ln = 5 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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