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

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


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

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

Reorder the terms:
lnx + -2ln(-4 + x) = -1ln(2)
lnx + (-4 * -2ln + x * -2ln) = -1ln(2)
lnx + (8ln + -2lnx) = -1ln(2)

Reorder the terms:
8ln + lnx + -2lnx = -1ln(2)

Combine like terms: lnx + -2lnx = -1lnx
8ln + -1lnx = -1ln(2)

Reorder the terms for easier multiplication:
8ln + -1lnx = -1 * 2ln

Multiply -1 * 2
8ln + -1lnx = -2ln

Solving
8ln + -1lnx = -2ln

Solving for variable 'l'.

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

Add '2ln' to each side of the equation.
8ln + 2ln + -1lnx = -2ln + 2ln

Combine like terms: 8ln + 2ln = 10ln
10ln + -1lnx = -2ln + 2ln

Combine like terms: -2ln + 2ln = 0
10ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Add 'x' to each side of the equation.
-1x + x = -10 + x

Combine like terms: -1x + x = 0
0 = -10 + x

Simplifying
0 = -10 + 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.

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