-ln(2x)-ln(x+4)=-ln(x)-ln(x+20)

Solution for -ln(2x)-ln(x+4)=-ln(x)-ln(x+20) equation:

Simplifying
-1ln(2x) + -1ln(x + 4) = -1ln(x) + -1ln(x + 20)

Remove parenthesis around (2x)
-1ln * 2x + -1ln(x + 4) = -1ln(x) + -1ln(x + 20)

Reorder the terms for easier multiplication:
-1 * 2ln * x + -1ln(x + 4) = -1ln(x) + -1ln(x + 20)

Multiply -1 * 2
-2ln * x + -1ln(x + 4) = -1ln(x) + -1ln(x + 20)

Multiply ln * x
-2lnx + -1ln(x + 4) = -1ln(x) + -1ln(x + 20)

Reorder the terms:
-2lnx + -1ln(4 + x) = -1ln(x) + -1ln(x + 20)
-2lnx + (4 * -1ln + x * -1ln) = -1ln(x) + -1ln(x + 20)
-2lnx + (-4ln + -1lnx) = -1ln(x) + -1ln(x + 20)

Reorder the terms:
-4ln + -2lnx + -1lnx = -1ln(x) + -1ln(x + 20)

Combine like terms: -2lnx + -1lnx = -3lnx
-4ln + -3lnx = -1ln(x) + -1ln(x + 20)

Multiply ln * x
-4ln + -3lnx = -1lnx + -1ln(x + 20)

Reorder the terms:
-4ln + -3lnx = -1lnx + -1ln(20 + x)
-4ln + -3lnx = -1lnx + (20 * -1ln + x * -1ln)
-4ln + -3lnx = -1lnx + (-20ln + -1lnx)

Reorder the terms:
-4ln + -3lnx = -20ln + -1lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
-4ln + -3lnx = -20ln + -2lnx

Solving
-4ln + -3lnx = -20ln + -2lnx

Solving for variable 'l'.

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

Add '20ln' to each side of the equation.
-4ln + 20ln + -3lnx = -20ln + 20ln + -2lnx

Combine like terms: -4ln + 20ln = 16ln
16ln + -3lnx = -20ln + 20ln + -2lnx

Combine like terms: -20ln + 20ln = 0
16ln + -3lnx = 0 + -2lnx
16ln + -3lnx = -2lnx

Add '2lnx' to each side of the equation.
16ln + -3lnx + 2lnx = -2lnx + 2lnx

Combine like terms: -3lnx + 2lnx = -1lnx
16ln + -1lnx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
16ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(16 + -1x) = 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 '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Add 'x' to each side of the equation.
-1x + x = -16 + x

Combine like terms: -1x + x = 0
0 = -16 + x

Simplifying
0 = -16 + x

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.