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

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

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

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

Multiply ln * x
8nL + 3nxL + -1lnx = ln(4)

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

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

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

Solving for variable 'l'.

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

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

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

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

Add '-8nL' to each side of the equation.
-4ln + -1lnx + 8nL + -8nL + 3nxL = 0 + -8nL

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4l + -1lx + 8L + 3xL) = 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 + 8L + 3xL)' equal to zero and attempt to solve:

Simplifying
-4l + -1lx + 8L + 3xL = 0

Reorder the terms:
8L + -4l + -1lx + 3xL = 0

Solving
8L + -4l + -1lx + 3xL = 0

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

Add '-8L' to each side of the equation.
8L + -4l + -1lx + -8L + 3xL = 0 + -8L

Reorder the terms:
8L + -8L + -4l + -1lx + 3xL = 0 + -8L

Combine like terms: 8L + -8L = 0
0 + -4l + -1lx + 3xL = 0 + -8L
-4l + -1lx + 3xL = 0 + -8L
Remove the zero:
-4l + -1lx + 3xL = -8L

Add '-3xL' to each side of the equation.
-4l + -1lx + 3xL + -3xL = -8L + -3xL

Combine like terms: 3xL + -3xL = 0
-4l + -1lx + 0 = -8L + -3xL
-4l + -1lx = -8L + -3xL

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.