Ln(5)-ln(x)=ln(x-4)

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


Simplifying
Ln(5) + -1ln(x) = ln(x + -4)

Reorder the terms for easier multiplication:
5nL + -1ln(x) = ln(x + -4)

Multiply ln * x
5nL + -1lnx = ln(x + -4)

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

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

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

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 + 4ln + 5nL = -4ln + 4ln + lnx

Reorder the terms:
4ln + -1lnx + 5nL = -4ln + 4ln + lnx

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

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

Combine like terms: -1lnx + -1lnx = -2lnx
4ln + -2lnx + 5nL = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
4ln + -2lnx + 5nL = 0

Add '-5nL' to each side of the equation.
4ln + -2lnx + 5nL + -5nL = 0 + -5nL

Combine like terms: 5nL + -5nL = 0
4ln + -2lnx + 0 = 0 + -5nL
4ln + -2lnx = 0 + -5nL
Remove the zero:
4ln + -2lnx = -5nL

Combine like terms: -5nL + 5nL = 0
4ln + -2lnx + 5nL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(4l + -2lx + 5L) = 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 + -2lx + 5L)' equal to zero and attempt to solve:

Simplifying
4l + -2lx + 5L = 0

Reorder the terms:
5L + 4l + -2lx = 0

Solving
5L + 4l + -2lx = 0

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

Add '-5L' to each side of the equation.
5L + 4l + -5L + -2lx = 0 + -5L

Reorder the terms:
5L + -5L + 4l + -2lx = 0 + -5L

Combine like terms: 5L + -5L = 0
0 + 4l + -2lx = 0 + -5L
4l + -2lx = 0 + -5L
Remove the zero:
4l + -2lx = -5L

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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