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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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