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Simplifying lny = 2ln(3 + 5x) lny = (3 * 2ln + 5x * 2ln) lny = (6ln + 10lnx) Solving lny = 6ln + 10lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -6ln + lny = 6ln + -6ln + 10lnx Combine like terms: 6ln + -6ln = 0 -6ln + lny = 0 + 10lnx -6ln + lny = 10lnx Add '-10lnx' to each side of the equation. -6ln + -10lnx + lny = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 -6ln + -10lnx + lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-6 + -10x + y) = 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 '(-6 + -10x + y)' equal to zero and attempt to solve: Simplifying -6 + -10x + y = 0 Solving -6 + -10x + y = 0 Move all terms containing l to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -10x + 6 + y = 0 + 6 Reorder the terms: -6 + 6 + -10x + y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -10x + y = 0 + 6 -10x + y = 0 + 6 Combine like terms: 0 + 6 = 6 -10x + y = 6 Add '10x' to each side of the equation. -10x + 10x + y = 6 + 10x Combine like terms: -10x + 10x = 0 0 + y = 6 + 10x y = 6 + 10x Add '-1y' to each side of the equation. y + -1y = 6 + 10x + -1y Combine like terms: y + -1y = 0 0 = 6 + 10x + -1y Simplifying 0 = 6 + 10x + -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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