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

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


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

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

Multiply ln * x
-1ln + 2lnx + lnx = ln(3)

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

Reorder the terms for easier multiplication:
-1ln + 3lnx = 3ln

Solving
-1ln + 3lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-1ln + -3ln + 3lnx = 3ln + -3ln

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-4 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 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 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Add '-3x' to each side of the equation.
3x + -3x = 4 + -3x

Combine like terms: 3x + -3x = 0
0 = 4 + -3x

Simplifying
0 = 4 + -3x

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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