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Simplifying -4ln(t2 + -9) + ln(5t) = 3ln(t + 3) Reorder the terms: -4ln(-9 + t2) + ln(5t) = 3ln(t + 3) (-9 * -4ln + t2 * -4ln) + ln(5t) = 3ln(t + 3) (36ln + -4lnt2) + ln(5t) = 3ln(t + 3) Remove parenthesis around (5t) 36ln + -4lnt2 + ln * 5t = 3ln(t + 3) Reorder the terms for easier multiplication: 36ln + -4lnt2 + 5ln * t = 3ln(t + 3) Multiply ln * t 36ln + -4lnt2 + 5lnt = 3ln(t + 3) Reorder the terms: 36ln + 5lnt + -4lnt2 = 3ln(t + 3) Reorder the terms: 36ln + 5lnt + -4lnt2 = 3ln(3 + t) 36ln + 5lnt + -4lnt2 = (3 * 3ln + t * 3ln) 36ln + 5lnt + -4lnt2 = (9ln + 3lnt) Solving 36ln + 5lnt + -4lnt2 = 9ln + 3lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 36ln + 5lnt + -9ln + -4lnt2 = 9ln + -9ln + 3lnt Reorder the terms: 36ln + -9ln + 5lnt + -4lnt2 = 9ln + -9ln + 3lnt Combine like terms: 36ln + -9ln = 27ln 27ln + 5lnt + -4lnt2 = 9ln + -9ln + 3lnt Combine like terms: 9ln + -9ln = 0 27ln + 5lnt + -4lnt2 = 0 + 3lnt 27ln + 5lnt + -4lnt2 = 3lnt Add '-3lnt' to each side of the equation. 27ln + 5lnt + -3lnt + -4lnt2 = 3lnt + -3lnt Combine like terms: 5lnt + -3lnt = 2lnt 27ln + 2lnt + -4lnt2 = 3lnt + -3lnt Combine like terms: 3lnt + -3lnt = 0 27ln + 2lnt + -4lnt2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(27 + 2t + -4t2) = 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 '(27 + 2t + -4t2)' equal to zero and attempt to solve: Simplifying 27 + 2t + -4t2 = 0 Solving 27 + 2t + -4t2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + 2t + -27 + -4t2 = 0 + -27 Reorder the terms: 27 + -27 + 2t + -4t2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 2t + -4t2 = 0 + -27 2t + -4t2 = 0 + -27 Combine like terms: 0 + -27 = -27 2t + -4t2 = -27 Add '-2t' to each side of the equation. 2t + -2t + -4t2 = -27 + -2t Combine like terms: 2t + -2t = 0 0 + -4t2 = -27 + -2t -4t2 = -27 + -2t Add '4t2' to each side of the equation. -4t2 + 4t2 = -27 + -2t + 4t2 Combine like terms: -4t2 + 4t2 = 0 0 = -27 + -2t + 4t2 Simplifying 0 = -27 + -2t + 4t2 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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