ln(84-28x)-ln(2)=2ln(x)

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Solution for ln(84-28x)-ln(2)=2ln(x) equation:


Simplifying
ln(84 + -28x) + -1ln(2) = 2ln(x)
(84 * ln + -28x * ln) + -1ln(2) = 2ln(x)
(84ln + -28lnx) + -1ln(2) = 2ln(x)

Reorder the terms for easier multiplication:
84ln + -28lnx + -1 * 2ln = 2ln(x)

Multiply -1 * 2
84ln + -28lnx + -2ln = 2ln(x)

Reorder the terms:
84ln + -2ln + -28lnx = 2ln(x)

Combine like terms: 84ln + -2ln = 82ln
82ln + -28lnx = 2ln(x)

Multiply ln * x
82ln + -28lnx = 2lnx

Solving
82ln + -28lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
82ln + -28lnx + -2lnx = 2lnx + -2lnx

Combine like terms: -28lnx + -2lnx = -30lnx
82ln + -30lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
82ln + -30lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(41 + -15x) = 0

Ignore the factor 2.

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 '(41 + -15x)' equal to zero and attempt to solve: Simplifying 41 + -15x = 0 Solving 41 + -15x = 0 Move all terms containing l to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + -15x = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -15x = 0 + -41 -15x = 0 + -41 Combine like terms: 0 + -41 = -41 -15x = -41 Add '15x' to each side of the equation. -15x + 15x = -41 + 15x Combine like terms: -15x + 15x = 0 0 = -41 + 15x Simplifying 0 = -41 + 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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