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