2ln(x-2)-ln(3x-8)=0

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Solution for 2ln(x-2)-ln(3x-8)=0 equation: 


Simplifying
2ln(x + -2) + -1ln(3x + -8) = 0

Reorder the terms:
2ln(-2 + x) + -1ln(3x + -8) = 0
(-2 * 2ln + x * 2ln) + -1ln(3x + -8) = 0
(-4ln + 2lnx) + -1ln(3x + -8) = 0

Reorder the terms:
-4ln + 2lnx + -1ln(-8 + 3x) = 0
-4ln + 2lnx + (-8 * -1ln + 3x * -1ln) = 0
-4ln + 2lnx + (8ln + -3lnx) = 0

Reorder the terms:
-4ln + 8ln + 2lnx + -3lnx = 0

Combine like terms: -4ln + 8ln = 4ln
4ln + 2lnx + -3lnx = 0

Combine like terms: 2lnx + -3lnx = -1lnx
4ln + -1lnx = 0

Solving
4ln + -1lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(4 + -1x) = 0


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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Add 'x' to each side of the equation.
-1x + x = -4 + x

Combine like terms: -1x + x = 0
0 = -4 + x

Simplifying
0 = -4 + x

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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