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Simplifying 5ln(x + y) + -2ln(y) + -8ln(x) = 0 (x * 5ln + y * 5ln) + -2ln(y) + -8ln(x) = 0 (5lnx + 5lny) + -2ln(y) + -8ln(x) = 0 Multiply ln * y 5lnx + 5lny + -2lny + -8ln(x) = 0 Multiply ln * x 5lnx + 5lny + -2lny + -8lnx = 0 Reorder the terms: 5lnx + -8lnx + 5lny + -2lny = 0 Combine like terms: 5lnx + -8lnx = -3lnx -3lnx + 5lny + -2lny = 0 Combine like terms: 5lny + -2lny = 3lny -3lnx + 3lny = 0 Solving -3lnx + 3lny = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-1x + y) = 0 Ignore the factor 3.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 '(-1x + y)' equal to zero and attempt to solve: Simplifying -1x + y = 0 Solving -1x + y = 0 Move all terms containing l to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + x + y = 0 + x Combine like terms: -1x + x = 0 0 + y = 0 + x y = 0 + x Remove the zero: y = x Add '-1y' to each side of the equation. y + -1y = x + -1y Combine like terms: y + -1y = 0 0 = x + -1y Simplifying 0 = x + -1y 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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