ln(ln(2x))=ln(12)

Solution for ln(ln(2x))=ln(12) equation:

Simplifying
ln(ln(2x)) = ln(12)

Remove parenthesis around (2x)
ln(ln * 2x) = ln(12)

Reorder the terms for easier multiplication:
ln(2ln * x) = ln(12)

Multiply ln * x
ln(2lnx) = ln(12)

Remove parenthesis around (2lnx)
ln * 2lnx = ln(12)

Reorder the terms for easier multiplication:
2ln * lnx = ln(12)

Multiply ln * lnx
2l2n2x = ln(12)

Reorder the terms for easier multiplication:
2l2n2x = 12ln

Solving
2l2n2x = 12ln

Solving for variable 'l'.

Reorder the terms:
-12ln + 2l2n2x = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-12ln + 2l2n2x = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-6 + lnx) = 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 '(-6 + lnx)' equal to zero and attempt to solve:

Simplifying
-6 + lnx = 0

Solving
-6 + lnx = 0

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

Add '6' to each side of the equation.
-6 + 6 + lnx = 0 + 6

Combine like terms: -6 + 6 = 0
0 + lnx = 0 + 6
lnx = 0 + 6

Combine like terms: 0 + 6 = 6
lnx = 6

Divide each side by 'nx'.
l = 6n-1x-1

Simplifying
l = 6n-1x-1
Solution
l = {6n-1x-1}