2*ln*x=ln*(x+6)+ln*3

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Solution for 2*ln*x=ln*(x+6)+ln*3 equation: 


Simplifying
2ln * x = ln(x + 6) + ln * 3

Multiply ln * x
2lnx = ln(x + 6) + ln * 3

Reorder the terms:
2lnx = ln(6 + x) + ln * 3
2lnx = (6 * ln + x * ln) + ln * 3
2lnx = (6ln + lnx) + ln * 3

Reorder the terms for easier multiplication:
2lnx = 6ln + lnx + 3ln

Reorder the terms:
2lnx = 6ln + 3ln + lnx

Combine like terms: 6ln + 3ln = 9ln
2lnx = 9ln + lnx

Solving
2lnx = 9ln + lnx

Solving for variable 'l'.

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

Add '-9ln' to each side of the equation.
-9ln + 2lnx = 9ln + -9ln + lnx

Combine like terms: 9ln + -9ln = 0
-9ln + 2lnx = 0 + lnx
-9ln + 2lnx = lnx

Add '-1lnx' to each side of the equation.
-9ln + 2lnx + -1lnx = lnx + -1lnx

Combine like terms: 2lnx + -1lnx = 1lnx
-9ln + 1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-9ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Add '-1x' to each side of the equation.
x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
0 = 9 + -1x

Simplifying
0 = 9 + -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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