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

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


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

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

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

Reorder the terms for easier multiplication:
12ln + -7lnx = 2ln

Solving
12ln + -7lnx = 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.
12ln + -2ln + -7lnx = 2ln + -2ln

Combine like terms: 12ln + -2ln = 10ln
10ln + -7lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
10ln + -7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + -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 '(10 + -7x)' equal to zero and attempt to solve:

Simplifying
10 + -7x = 0

Solving
10 + -7x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -7x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7x = 0 + -10
-7x = 0 + -10

Combine like terms: 0 + -10 = -10
-7x = -10

Add '7x' to each side of the equation.
-7x + 7x = -10 + 7x

Combine like terms: -7x + 7x = 0
0 = -10 + 7x

Simplifying
0 = -10 + 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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