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Simplifying 6lny = 3lne2 + -9lnx Solving 6lny = 3e2ln + -9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3e2ln' to each side of the equation. -3e2ln + 6lny = 3e2ln + -3e2ln + -9lnx Combine like terms: 3e2ln + -3e2ln = 0 -3e2ln + 6lny = 0 + -9lnx -3e2ln + 6lny = -9lnx Add '9lnx' to each side of the equation. -3e2ln + 9lnx + 6lny = -9lnx + 9lnx Combine like terms: -9lnx + 9lnx = 0 -3e2ln + 9lnx + 6lny = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-1e2 + 3x + 2y) = 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 '(-1e2 + 3x + 2y)' equal to zero and attempt to solve: Simplifying -1e2 + 3x + 2y = 0 Solving -1e2 + 3x + 2y = 0 Move all terms containing l to the left, all other terms to the right. Add 'e2' to each side of the equation. -1e2 + 3x + e2 + 2y = 0 + e2 Reorder the terms: -1e2 + e2 + 3x + 2y = 0 + e2 Combine like terms: -1e2 + e2 = 0 0 + 3x + 2y = 0 + e2 3x + 2y = 0 + e2 Remove the zero: 3x + 2y = e2 Add '-3x' to each side of the equation. 3x + -3x + 2y = e2 + -3x Combine like terms: 3x + -3x = 0 0 + 2y = e2 + -3x 2y = e2 + -3x Add '-2y' to each side of the equation. 2y + -2y = e2 + -3x + -2y Combine like terms: 2y + -2y = 0 0 = e2 + -3x + -2y Simplifying 0 = e2 + -3x + -2y 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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