2ln(lnx)-ln(5lnx-6)=0

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Solution for 2ln(lnx)-ln(5lnx-6)=0 equation: 


Simplifying
2ln(lnx) + -1ln(5lnx + -6) = 0

Multiply ln * lnx
2l2n2x + -1ln(5lnx + -6) = 0

Reorder the terms:
2l2n2x + -1ln(-6 + 5lnx) = 0
2l2n2x + (-6 * -1ln + 5lnx * -1ln) = 0
2l2n2x + (6ln + -5l2n2x) = 0

Reorder the terms:
6ln + 2l2n2x + -5l2n2x = 0

Combine like terms: 2l2n2x + -5l2n2x = -3l2n2x
6ln + -3l2n2x = 0

Solving
6ln + -3l2n2x = 0

Solving for variable 'l'.

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(2 + -1lnx) = 0

Ignore the factor 3.

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 '(2 + -1lnx)' equal to zero and attempt to solve:

Simplifying
2 + -1lnx = 0

Solving
2 + -1lnx = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1lnx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1lnx = 0 + -2
-1lnx = 0 + -2

Combine like terms: 0 + -2 = -2
-1lnx = -2

Divide each side by '-1nx'.
l = 2n-1x-1

Simplifying
l = 2n-1x-1
Solution
l = {2n-1x-1}

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