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

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


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

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

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

Solving
-1ln + 4lnx = lnx

Solving for variable 'l'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 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 '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 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 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

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

Combine like terms: 3x + -3x = 0
0 = 1 + -3x

Simplifying
0 = 1 + -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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