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

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


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

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

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

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

Combine like terms: 3ln + 6ln = 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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