ln(9-3x)-2ln(x)=ln(2)

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Solution for ln(9-3x)-2ln(x)=ln(2) equation: 


Simplifying
ln(9 + -3x) + -2ln(x) = ln(2)
(9 * ln + -3x * ln) + -2ln(x) = ln(2)
(9ln + -3lnx) + -2ln(x) = ln(2)

Multiply ln * x
9ln + -3lnx + -2lnx = ln(2)

Combine like terms: -3lnx + -2lnx = -5lnx
9ln + -5lnx = ln(2)

Reorder the terms for easier multiplication:
9ln + -5lnx = 2ln

Solving
9ln + -5lnx = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
9ln + -2ln + -5lnx = 2ln + -2ln

Combine like terms: 9ln + -2ln = 7ln
7ln + -5lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
7ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + -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 '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Add '5x' to each side of the equation.
-5x + 5x = -7 + 5x

Combine like terms: -5x + 5x = 0
0 = -7 + 5x

Simplifying
0 = -7 + 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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