Ln(x+3)-ln(x-4)=ln(8)

Solution for Ln(x+3)-ln(x-4)=ln(8) equation:

Simplifying
Ln(x + 3) + -1ln(x + -4) = ln(8)

Reorder the terms:
nL(3 + x) + -1ln(x + -4) = ln(8)
(3 * nL + x * nL) + -1ln(x + -4) = ln(8)
(3nL + nxL) + -1ln(x + -4) = ln(8)

Reorder the terms:
3nL + nxL + -1ln(-4 + x) = ln(8)
3nL + nxL + (-4 * -1ln + x * -1ln) = ln(8)
3nL + nxL + (4ln + -1lnx) = ln(8)

Reorder the terms:
4ln + -1lnx + 3nL + nxL = ln(8)

Reorder the terms for easier multiplication:
4ln + -1lnx + 3nL + nxL = 8ln

Solving
4ln + -1lnx + 3nL + nxL = 8ln

Solving for variable 'l'.

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

Add '-8ln' to each side of the equation.
4ln + -1lnx + 3nL + -8ln + nxL = 8ln + -8ln

Reorder the terms:
4ln + -8ln + -1lnx + 3nL + nxL = 8ln + -8ln

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

Combine like terms: 8ln + -8ln = 0
-4ln + -1lnx + 3nL + nxL = 0

Add '-3nL' to each side of the equation.
-4ln + -1lnx + 3nL + -3nL + nxL = 0 + -3nL

Combine like terms: 3nL + -3nL = 0
-4ln + -1lnx + 0 + nxL = 0 + -3nL
-4ln + -1lnx + nxL = 0 + -3nL
Remove the zero:
-4ln + -1lnx + nxL = -3nL

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

Combine like terms: nxL + -1nxL = 0
-4ln + -1lnx + 0 = -3nL + -1nxL
-4ln + -1lnx = -3nL + -1nxL

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

Combine like terms: -3nL + 3nL = 0
-4ln + -1lnx + 3nL + nxL = 0 + -1nxL + nxL
-4ln + -1lnx + 3nL + nxL = -1nxL + nxL

Combine like terms: -1nxL + nxL = 0
-4ln + -1lnx + 3nL + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4l + -1lx + 3L + xL) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

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 '(-4l + -1lx + 3L + xL)' equal to zero and attempt to solve:

Simplifying
-4l + -1lx + 3L + xL = 0

Reorder the terms:
3L + -4l + -1lx + xL = 0

Solving
3L + -4l + -1lx + xL = 0

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

Add '-3L' to each side of the equation.
3L + -4l + -1lx + -3L + xL = 0 + -3L

Reorder the terms:
3L + -3L + -4l + -1lx + xL = 0 + -3L

Combine like terms: 3L + -3L = 0
0 + -4l + -1lx + xL = 0 + -3L
-4l + -1lx + xL = 0 + -3L
Remove the zero:
-4l + -1lx + xL = -3L

Add '-1xL' to each side of the equation.
-4l + -1lx + xL + -1xL = -3L + -1xL

Combine like terms: xL + -1xL = 0
-4l + -1lx + 0 = -3L + -1xL
-4l + -1lx = -3L + -1xL

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.