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Simplifying ln(t + 1) = ln(3)(t + -4) Reorder the terms: ln(1 + t) = ln(3)(t + -4) (1 * ln + t * ln) = ln(3)(t + -4) (1ln + lnt) = ln(3)(t + -4) Reorder the terms: 1ln + lnt = ln * 3(-4 + t) Reorder the terms for easier multiplication: 1ln + lnt = 3ln(-4 + t) 1ln + lnt = (-4 * 3ln + t * 3ln) 1ln + lnt = (-12ln + 3lnt) Solving 1ln + lnt = -12ln + 3lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 1ln + 12ln + lnt = -12ln + 12ln + 3lnt Combine like terms: 1ln + 12ln = 13ln 13ln + lnt = -12ln + 12ln + 3lnt Combine like terms: -12ln + 12ln = 0 13ln + lnt = 0 + 3lnt 13ln + lnt = 3lnt Add '-3lnt' to each side of the equation. 13ln + lnt + -3lnt = 3lnt + -3lnt Combine like terms: lnt + -3lnt = -2lnt 13ln + -2lnt = 3lnt + -3lnt Combine like terms: 3lnt + -3lnt = 0 13ln + -2lnt = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(13 + -2t) = 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 '(13 + -2t)' equal to zero and attempt to solve: Simplifying 13 + -2t = 0 Solving 13 + -2t = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2t = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2t = 0 + -13 -2t = 0 + -13 Combine like terms: 0 + -13 = -13 -2t = -13 Add '2t' to each side of the equation. -2t + 2t = -13 + 2t Combine like terms: -2t + 2t = 0 0 = -13 + 2t Simplifying 0 = -13 + 2t 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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