ln(5x-2)-ln(3x+2)=0

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Solution for ln(5x-2)-ln(3x+2)=0 equation: 


Simplifying
ln(5x + -2) + -1ln(3x + 2) = 0

Reorder the terms:
ln(-2 + 5x) + -1ln(3x + 2) = 0
(-2 * ln + 5x * ln) + -1ln(3x + 2) = 0
(-2ln + 5lnx) + -1ln(3x + 2) = 0

Reorder the terms:
-2ln + 5lnx + -1ln(2 + 3x) = 0
-2ln + 5lnx + (2 * -1ln + 3x * -1ln) = 0
-2ln + 5lnx + (-2ln + -3lnx) = 0

Reorder the terms:
-2ln + -2ln + 5lnx + -3lnx = 0

Combine like terms: -2ln + -2ln = -4ln
-4ln + 5lnx + -3lnx = 0

Combine like terms: 5lnx + -3lnx = 2lnx
-4ln + 2lnx = 0

Solving
-4ln + 2lnx = 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), '2ln'.
2ln(-2 + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

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

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

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

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

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

Simplifying
0 = 2 + -1x

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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