Ln(x)-ln(x-7)=ln(3)

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Solution for Ln(x)-ln(x-7)=ln(3) equation: 


Simplifying
Ln(x) + -1ln(x + -7) = ln(3)

Multiply nL * x
nxL + -1ln(x + -7) = ln(3)

Reorder the terms:
nxL + -1ln(-7 + x) = ln(3)
nxL + (-7 * -1ln + x * -1ln) = ln(3)
nxL + (7ln + -1lnx) = ln(3)

Reorder the terms:
7ln + -1lnx + nxL = ln(3)

Reorder the terms for easier multiplication:
7ln + -1lnx + nxL = 3ln

Solving
7ln + -1lnx + nxL = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
7ln + -1lnx + -3ln + nxL = 3ln + -3ln

Reorder the terms:
7ln + -3ln + -1lnx + nxL = 3ln + -3ln

Combine like terms: 7ln + -3ln = 4ln
4ln + -1lnx + nxL = 3ln + -3ln

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

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

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

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

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

Simplifying
4l + -1lx + xL = 0

Solving
4l + -1lx + xL = 0

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

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

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

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