ln(12-5x)-2ln(x)=ln(3)

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Solution for ln(12-5x)-2ln(x)=ln(3) equation: 


Simplifying
ln(12 + -5x) + -2ln(x) = ln(3)
(12 * ln + -5x * ln) + -2ln(x) = ln(3)
(12ln + -5lnx) + -2ln(x) = ln(3)

Multiply ln * x
12ln + -5lnx + -2lnx = ln(3)

Combine like terms: -5lnx + -2lnx = -7lnx
12ln + -7lnx = ln(3)

Reorder the terms for easier multiplication:
12ln + -7lnx = 3ln

Solving
12ln + -7lnx = 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.
12ln + -3ln + -7lnx = 3ln + -3ln

Combine like terms: 12ln + -3ln = 9ln
9ln + -7lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
9ln + -7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(9 + -7x) = 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 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 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 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Add '7x' to each side of the equation.
-7x + 7x = -9 + 7x

Combine like terms: -7x + 7x = 0
0 = -9 + 7x

Simplifying
0 = -9 + 7x

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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