2ln(x-6)=lnx

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


Simplifying
2ln(x + -6) = lnx

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

Solving
-12ln + 2lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
-12ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-12ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-12ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-12 + x) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

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 '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + x = 0 + 12
x = 0 + 12

Combine like terms: 0 + 12 = 12
x = 12

Add '-1x' to each side of the equation.
x + -1x = 12 + -1x

Combine like terms: x + -1x = 0
0 = 12 + -1x

Simplifying
0 = 12 + -1x

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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