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