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

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Solution for ln(2x-1)+ln(3x)=0 equation: 


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

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

Remove parenthesis around (3x)
-1ln + 2lnx + ln * 3x = 0

Reorder the terms for easier multiplication:
-1ln + 2lnx + 3ln * x = 0

Multiply ln * x
-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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