ln(12-13x)-2ln(x)=ln(4)

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Solution for ln(12-13x)-2ln(x)=ln(4) equation: 


Simplifying
ln(12 + -13x) + -2ln(x) = ln(4)
(12 * ln + -13x * ln) + -2ln(x) = ln(4)
(12ln + -13lnx) + -2ln(x) = ln(4)

Multiply ln * x
12ln + -13lnx + -2lnx = ln(4)

Combine like terms: -13lnx + -2lnx = -15lnx
12ln + -15lnx = ln(4)

Reorder the terms for easier multiplication:
12ln + -15lnx = 4ln

Solving
12ln + -15lnx = 4ln

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
12ln + -4ln + -15lnx = 4ln + -4ln

Combine like terms: 12ln + -4ln = 8ln
8ln + -15lnx = 4ln + -4ln

Combine like terms: 4ln + -4ln = 0
8ln + -15lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -15x) = 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 '(8 + -15x)' equal to zero and attempt to solve:

Simplifying
8 + -15x = 0

Solving
8 + -15x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -15x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -15x = 0 + -8
-15x = 0 + -8

Combine like terms: 0 + -8 = -8
-15x = -8

Add '15x' to each side of the equation.
-15x + 15x = -8 + 15x

Combine like terms: -15x + 15x = 0
0 = -8 + 15x

Simplifying
0 = -8 + 15x

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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