Lnx=2ln(x-6)

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Solution for Lnx=2ln(x-6) equation: 


Simplifying
Lnx = 2ln(x + -6)

Reorder the terms:
nxL = 2ln(-6 + x)
nxL = (-6 * 2ln + x * 2ln)
nxL = (-12ln + 2lnx)

Solving
nxL = -12ln + 2lnx

Solving for variable 'n'.

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

Add '12ln' to each side of the equation.
12ln + nxL = -12ln + 12ln + 2lnx

Combine like terms: -12ln + 12ln = 0
12ln + nxL = 0 + 2lnx
12ln + nxL = 2lnx

Add '-2lnx' to each side of the equation.
12ln + -2lnx + nxL = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
12ln + -2lnx + nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(12l + -2lx + 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 n to the left, all other terms to the right.

Simplifying
n = 0

Subproblem 2
Set the factor '(12l + -2lx + xL)' equal to zero and attempt to solve:

Simplifying
12l + -2lx + xL = 0

Solving
12l + -2lx + xL = 0

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

Add '-12l' to each side of the equation.
12l + -2lx + -12l + xL = 0 + -12l

Reorder the terms:
12l + -12l + -2lx + xL = 0 + -12l

Combine like terms: 12l + -12l = 0
0 + -2lx + xL = 0 + -12l
-2lx + xL = 0 + -12l
Remove the zero:
-2lx + xL = -12l

Add '2lx' to each side of the equation.
-2lx + 2lx + xL = -12l + 2lx

Combine like terms: -2lx + 2lx = 0
0 + xL = -12l + 2lx
xL = -12l + 2lx

Add '-1xL' to each side of the equation.
xL + -1xL = -12l + 2lx + -1xL

Combine like terms: xL + -1xL = 0
0 = -12l + 2lx + -1xL

Simplifying
0 = -12l + 2lx + -1xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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