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

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

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

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

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

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

Solving
-4ln + 2lnx = 2

Solving for variable 'l'.

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

Reorder the terms:
-2 + -4ln + 2lnx = 2 + -2

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -2ln + lnx)' equal to zero and attempt to solve:

Simplifying
-1 + -2ln + lnx = 0

Solving
-1 + -2ln + lnx = 0

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

Add '1' to each side of the equation.
-1 + -2ln + 1 + lnx = 0 + 1

Reorder the terms:
-1 + 1 + -2ln + lnx = 0 + 1

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

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

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.