3*ln(x)-ln(x)=ln(9)

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Solution for 3*ln(x)-ln(x)=ln(9) equation: 


Simplifying
3ln(x) + -1ln(x) = ln(9)

Multiply ln * x
3lnx + -1ln(x) = ln(9)

Multiply ln * x
3lnx + -1lnx = ln(9)

Combine like terms: 3lnx + -1lnx = 2lnx
2lnx = ln(9)

Reorder the terms for easier multiplication:
2lnx = 9ln

Solving
2lnx = 9ln

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
-9 + 2x = 0

Solving
-9 + 2x = 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 + 2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x = 0 + 9
2x = 0 + 9

Combine like terms: 0 + 9 = 9
2x = 9

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

Combine like terms: 2x + -2x = 0
0 = 9 + -2x

Simplifying
0 = 9 + -2x

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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