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