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

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


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

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

Combine like terms: -3lnx + -2lnx = -5lnx
6ln + -5lnx = ln(3)

Reorder the terms for easier multiplication:
6ln + -5lnx = 3ln

Solving
6ln + -5lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
6ln + -3ln + -5lnx = 3ln + -3ln

Combine like terms: 6ln + -3ln = 3ln
3ln + -5lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
3ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + -5x) = 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 '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Add '5x' to each side of the equation.
-5x + 5x = -3 + 5x

Combine like terms: -5x + 5x = 0
0 = -3 + 5x

Simplifying
0 = -3 + 5x

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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