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Simplifying ln(0.5) = tln(1 + -1a) Reorder the terms for easier multiplication: 0.5ln = tln(1 + -1a) 0.5ln = (1 * lnt + -1a * lnt) Reorder the terms: 0.5ln = (-1alnt + 1lnt) 0.5ln = (-1alnt + 1lnt) Solving 0.5ln = -1alnt + 1lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'alnt' to each side of the equation. alnt + 0.5ln = -1alnt + alnt + 1lnt Combine like terms: -1alnt + alnt = 0 alnt + 0.5ln = 0 + 1lnt alnt + 0.5ln = 1lnt Add '-1lnt' to each side of the equation. alnt + 0.5ln + -1lnt = 1lnt + -1lnt Combine like terms: 1lnt + -1lnt = 0 alnt + 0.5ln + -1lnt = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(at + 0.5 + -1t) = 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 '(at + 0.5 + -1t)' equal to zero and attempt to solve: Simplifying at + 0.5 + -1t = 0 Reorder the terms: 0.5 + at + -1t = 0 Solving 0.5 + at + -1t = 0 Move all terms containing l to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + at + -0.5 + -1t = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + at + -1t = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + at + -1t = 0 + -0.5 at + -1t = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 at + -1t = -0.5 Add '-1at' to each side of the equation. at + -1at + -1t = -0.5 + -1at Combine like terms: at + -1at = 0 0 + -1t = -0.5 + -1at -1t = -0.5 + -1at Add 't' to each side of the equation. -1t + t = -0.5 + -1at + t Combine like terms: -1t + t = 0 0 = -0.5 + -1at + t Simplifying 0 = -0.5 + -1at + t 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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