ln(5n+2)=ln-3n

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Solution for ln(5n+2)=ln-3n equation: 


Simplifying
ln(5n + 2) = ln + -3n

Reorder the terms:
ln(2 + 5n) = ln + -3n
(2 * ln + 5n * ln) = ln + -3n
(2ln + 5ln2) = ln + -3n

Solving
2ln + 5ln2 = ln + -3n

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
2ln + -1ln + 5ln2 = ln + -1ln + -3n

Combine like terms: 2ln + -1ln = 1ln
1ln + 5ln2 = ln + -1ln + -3n

Combine like terms: ln + -1ln = 0
1ln + 5ln2 = 0 + -3n
1ln + 5ln2 = -3n

Combine like terms: -3n + 3n = 0
1ln + 5ln2 + 3n = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(l + 5ln + 3) = 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 '(l + 5ln + 3)' equal to zero and attempt to solve:

Simplifying
l + 5ln + 3 = 0

Reorder the terms:
3 + l + 5ln = 0

Solving
3 + l + 5ln = 0

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

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

Reorder the terms:
3 + -3 + l + 5ln = 0 + -3

Combine like terms: 3 + -3 = 0
0 + l + 5ln = 0 + -3
l + 5ln = 0 + -3

Combine like terms: 0 + -3 = -3
l + 5ln = -3

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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