ln(3-x)+4=ln(x-5)

Solution for ln(3-x)+4=ln(x-5) equation:

Simplifying
ln(3 + -1x) + 4 = ln(x + -5)
(3 * ln + -1x * ln) + 4 = ln(x + -5)
(3ln + -1lnx) + 4 = ln(x + -5)

Reorder the terms:
4 + 3ln + -1lnx = ln(x + -5)

Reorder the terms:
4 + 3ln + -1lnx = ln(-5 + x)
4 + 3ln + -1lnx = (-5 * ln + x * ln)
4 + 3ln + -1lnx = (-5ln + lnx)

Solving
4 + 3ln + -1lnx = -5ln + lnx

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
4 + 3ln + 5ln + -1lnx = -5ln + 5ln + lnx

Combine like terms: 3ln + 5ln = 8ln
4 + 8ln + -1lnx = -5ln + 5ln + lnx

Combine like terms: -5ln + 5ln = 0
4 + 8ln + -1lnx = 0 + lnx
4 + 8ln + -1lnx = lnx

Add '-1lnx' to each side of the equation.
4 + 8ln + -1lnx + -1lnx = lnx + -1lnx

Combine like terms: -1lnx + -1lnx = -2lnx
4 + 8ln + -2lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
4 + 8ln + -2lnx = 0

Add '-4' to each side of the equation.
4 + 8ln + -4 + -2lnx = 0 + -4

Reorder the terms:
4 + -4 + 8ln + -2lnx = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 8ln + -2lnx = 0 + -4
8ln + -2lnx = 0 + -4

Combine like terms: 0 + -4 = -4
8ln + -2lnx = -4

Reorder the terms:
4 + 8ln + -2lnx = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 8ln + -2lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 4ln + -1lnx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 4ln + -1lnx)' equal to zero and attempt to solve:

Simplifying
2 + 4ln + -1lnx = 0

Solving
2 + 4ln + -1lnx = 0

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

Add '-2' to each side of the equation.
2 + 4ln + -2 + -1lnx = 0 + -2

Reorder the terms:
2 + -2 + 4ln + -1lnx = 0 + -2

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

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

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.