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Simplifying 4lnx + 5lny + -2lnz = 0 Solving 4lnx + 5lny + -2lnz = 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), 'ln'. ln(4x + 5y + -2z) = 0Subproblem 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 '(4x + 5y + -2z)' equal to zero and attempt to solve: Simplifying 4x + 5y + -2z = 0 Solving 4x + 5y + -2z = 0 Move all terms containing l to the left, all other terms to the right. Add '-4x' to each side of the equation. 4x + 5y + -4x + -2z = 0 + -4x Reorder the terms: 4x + -4x + 5y + -2z = 0 + -4x Combine like terms: 4x + -4x = 0 0 + 5y + -2z = 0 + -4x 5y + -2z = 0 + -4x Remove the zero: 5y + -2z = -4x Add '-5y' to each side of the equation. 5y + -5y + -2z = -4x + -5y Combine like terms: 5y + -5y = 0 0 + -2z = -4x + -5y -2z = -4x + -5y Add '2z' to each side of the equation. -2z + 2z = -4x + -5y + 2z Combine like terms: -2z + 2z = 0 0 = -4x + -5y + 2z Simplifying 0 = -4x + -5y + 2z 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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