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Simplifying 3lny = lne2 + 5lnx Solving 3lny = e2ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1e2ln' to each side of the equation. -1e2ln + 3lny = e2ln + -1e2ln + 5lnx Combine like terms: e2ln + -1e2ln = 0 -1e2ln + 3lny = 0 + 5lnx -1e2ln + 3lny = 5lnx Add '-5lnx' to each side of the equation. -1e2ln + -5lnx + 3lny = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -1e2ln + -5lnx + 3lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-1e2 + -5x + 3y) = 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 '(-1e2 + -5x + 3y)' equal to zero and attempt to solve: Simplifying -1e2 + -5x + 3y = 0 Solving -1e2 + -5x + 3y = 0 Move all terms containing l to the left, all other terms to the right. Add 'e2' to each side of the equation. -1e2 + -5x + e2 + 3y = 0 + e2 Reorder the terms: -1e2 + e2 + -5x + 3y = 0 + e2 Combine like terms: -1e2 + e2 = 0 0 + -5x + 3y = 0 + e2 -5x + 3y = 0 + e2 Remove the zero: -5x + 3y = e2 Add '5x' to each side of the equation. -5x + 5x + 3y = e2 + 5x Combine like terms: -5x + 5x = 0 0 + 3y = e2 + 5x 3y = e2 + 5x Add '-3y' to each side of the equation. 3y + -3y = e2 + 5x + -3y Combine like terms: 3y + -3y = 0 0 = e2 + 5x + -3y Simplifying 0 = e2 + 5x + -3y 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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