ln(6-4x)-2ln(x)=ln(2)

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Solution for ln(6-4x)-2ln(x)=ln(2) equation: 


Simplifying
ln(6 + -4x) + -2ln(x) = ln(2)
(6 * ln + -4x * ln) + -2ln(x) = ln(2)
(6ln + -4lnx) + -2ln(x) = ln(2)

Multiply ln * x
6ln + -4lnx + -2lnx = ln(2)

Combine like terms: -4lnx + -2lnx = -6lnx
6ln + -6lnx = ln(2)

Reorder the terms for easier multiplication:
6ln + -6lnx = 2ln

Solving
6ln + -6lnx = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
6ln + -2ln + -6lnx = 2ln + -2ln

Combine like terms: 6ln + -2ln = 4ln
4ln + -6lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
4ln + -6lnx = 0

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Add '3x' to each side of the equation.
-3x + 3x = -2 + 3x

Combine like terms: -3x + 3x = 0
0 = -2 + 3x

Simplifying
0 = -2 + 3x

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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