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

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


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

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

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

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

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

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

Solving
1ln + 4lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
1ln + 4lnx + -2lnx = 2lnx + -2lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -2x

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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