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Simplifying 90 = 40ln(2t + 1) Reorder the terms: 90 = 40ln(1 + 2t) 90 = (1 * 40ln + 2t * 40ln) 90 = (40ln + 80lnt) Solving 90 = 40ln + 80lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. 90 + -40ln = 40ln + -40ln + 80lnt Combine like terms: 40ln + -40ln = 0 90 + -40ln = 0 + 80lnt 90 + -40ln = 80lnt Add '-80lnt' to each side of the equation. 90 + -40ln + -80lnt = 80lnt + -80lnt Combine like terms: 80lnt + -80lnt = 0 90 + -40ln + -80lnt = 0 Add '-90' to each side of the equation. 90 + -40ln + -90 + -80lnt = 0 + -90 Reorder the terms: 90 + -90 + -40ln + -80lnt = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -40ln + -80lnt = 0 + -90 -40ln + -80lnt = 0 + -90 Combine like terms: 0 + -90 = -90 -40ln + -80lnt = -90 Reorder the terms: 90 + -40ln + -80lnt = -90 + 90 Combine like terms: -90 + 90 = 0 90 + -40ln + -80lnt = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(9 + -4ln + -8lnt) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(9 + -4ln + -8lnt)' equal to zero and attempt to solve: Simplifying 9 + -4ln + -8lnt = 0 Solving 9 + -4ln + -8lnt = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -4ln + -9 + -8lnt = 0 + -9 Reorder the terms: 9 + -9 + -4ln + -8lnt = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4ln + -8lnt = 0 + -9 -4ln + -8lnt = 0 + -9 Combine like terms: 0 + -9 = -9 -4ln + -8lnt = -9 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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