3*ln(2+ln*8)=2*ln(4x)

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Solution for 3*ln(2+ln*8)=2*ln(4x) equation: 


Simplifying
3ln(2 + ln * 8) = 2ln(4x)

Reorder the terms for easier multiplication:
3ln(2 + 8ln) = 2ln(4x)
(2 * 3ln + 8ln * 3ln) = 2ln(4x)
(6ln + 24l2n2) = 2ln(4x)

Remove parenthesis around (4x)
6ln + 24l2n2 = 2ln * 4x

Reorder the terms for easier multiplication:
6ln + 24l2n2 = 2 * 4ln * x

Multiply 2 * 4
6ln + 24l2n2 = 8ln * x

Multiply ln * x
6ln + 24l2n2 = 8lnx

Solving
6ln + 24l2n2 = 8lnx

Solving for variable 'l'.

Reorder the terms:
6ln + -8lnx + 24l2n2 = 8lnx + -8lnx

Combine like terms: 8lnx + -8lnx = 0
6ln + -8lnx + 24l2n2 = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(3 + -4x + 12ln) = 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 '(3 + -4x + 12ln)' equal to zero and attempt to solve:

Simplifying
3 + -4x + 12ln = 0

Reorder the terms:
3 + 12ln + -4x = 0

Solving
3 + 12ln + -4x = 0

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

Add '-3' to each side of the equation.
3 + 12ln + -3 + -4x = 0 + -3

Reorder the terms:
3 + -3 + 12ln + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 12ln + -4x = 0 + -3
12ln + -4x = 0 + -3

Combine like terms: 0 + -3 = -3
12ln + -4x = -3

Add '4x' to each side of the equation.
12ln + -4x + 4x = -3 + 4x

Combine like terms: -4x + 4x = 0
12ln + 0 = -3 + 4x
12ln = -3 + 4x

Divide each side by '12n'.
l = -0.25n-1 + 0.3333333333n-1x

Simplifying
l = -0.25n-1 + 0.3333333333n-1x
Solution
l = {-0.25n-1 + 0.3333333333n-1x}

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