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

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


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

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

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

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

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

Combine like terms: 2lnx + 3lnx = 5lnx
1ln + 5lnx = 0

Solving
1ln + 5lnx = 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(1 + 5x) = 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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Add '-5x' to each side of the equation.
5x + -5x = -1 + -5x

Combine like terms: 5x + -5x = 0
0 = -1 + -5x

Simplifying
0 = -1 + -5x

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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