ln(1-2x)+ln(2x)=ln(4x)

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Solution for ln(1-2x)+ln(2x)=ln(4x) equation: 


Simplifying
ln(1 + -2x) + ln(2x) = ln(4x)
(1 * ln + -2x * ln) + ln(2x) = ln(4x)
(1ln + -2lnx) + ln(2x) = ln(4x)

Remove parenthesis around (2x)
1ln + -2lnx + ln * 2x = ln(4x)

Reorder the terms for easier multiplication:
1ln + -2lnx + 2ln * x = ln(4x)

Multiply ln * x
1ln + -2lnx + 2lnx = ln(4x)

Combine like terms: -2lnx + 2lnx = 0
1ln + 0 = ln(4x)
1ln = ln(4x)

Remove parenthesis around (4x)
1ln = ln * 4x

Reorder the terms for easier multiplication:
1ln = 4ln * x

Multiply ln * x
1ln = 4lnx

Solving
1ln = 4lnx

Solving for variable 'l'.

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

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

Combine like terms: 4lnx + -4lnx = 0
1ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -4x) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

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

Combine like terms: -4x + 4x = 0
0 = -1 + 4x

Simplifying
0 = -1 + 4x

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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