Ln(4n+3)=2ln(2n)

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Solution for Ln(4n+3)=2ln(2n) equation: 


Simplifying
Ln(4n + 3) = 2ln(2n)

Reorder the terms:
nL(3 + 4n) = 2ln(2n)
(3 * nL + 4n * nL) = 2ln(2n)
(3nL + 4n2L) = 2ln(2n)

Remove parenthesis around (2n)
3nL + 4n2L = 2ln * 2n

Reorder the terms for easier multiplication:
3nL + 4n2L = 2 * 2ln * n

Multiply 2 * 2
3nL + 4n2L = 4ln * n

Multiply ln * n
3nL + 4n2L = 4ln2

Solving
3nL + 4n2L = 4ln2

Solving for variable 'n'.

Reorder the terms:
-4ln2 + 3nL + 4n2L = 4ln2 + -4ln2

Combine like terms: 4ln2 + -4ln2 = 0
-4ln2 + 3nL + 4n2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4ln + 3L + 4nL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-4ln + 3L + 4nL)' equal to zero and attempt to solve:

Simplifying
-4ln + 3L + 4nL = 0

Reorder the terms:
3L + -4ln + 4nL = 0

Solving
3L + -4ln + 4nL = 0

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

Add '-3L' to each side of the equation.
3L + -4ln + -3L + 4nL = 0 + -3L

Reorder the terms:
3L + -3L + -4ln + 4nL = 0 + -3L

Combine like terms: 3L + -3L = 0
0 + -4ln + 4nL = 0 + -3L
-4ln + 4nL = 0 + -3L
Remove the zero:
-4ln + 4nL = -3L

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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