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

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


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

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

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

Reorder the terms for easier multiplication:
1ln + -4lnx = 3ln

Solving
1ln + -4lnx = 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 + -4lnx = 3ln + -3ln

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

Combine like terms: 3ln + -3ln = 0
-2ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(1 + 2x) = 0

Ignore the factor -2.

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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