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

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


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

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

Reorder the terms:
-2ln + lnx + -2lnx = -1ln(4x)

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

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

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

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

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

Solving
-2ln + -1lnx = -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.
-2ln + -1lnx + 4lnx = -4lnx + 4lnx

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 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 '(-2 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Add '-3x' to each side of the equation.
3x + -3x = 2 + -3x

Combine like terms: 3x + -3x = 0
0 = 2 + -3x

Simplifying
0 = 2 + -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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