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Simplifying ln(y) = ln(x + C) Multiply ln * y lny = ln(x + C) Reorder the terms: lny = ln(C + x) lny = (C * ln + x * ln) lny = (lnC + lnx) Solving lny = lnC + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnC' to each side of the equation. -1lnC + lny = lnC + -1lnC + lnx Combine like terms: lnC + -1lnC = 0 -1lnC + lny = 0 + lnx -1lnC + lny = lnx Add '-1lnx' to each side of the equation. -1lnC + -1lnx + lny = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1lnC + -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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