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Simplifying 160 = 46 + 19ln(10t + 1) Reorder the terms: 160 = 46 + 19ln(1 + 10t) 160 = 46 + (1 * 19ln + 10t * 19ln) 160 = 46 + (19ln + 190lnt) Solving 160 = 46 + 19ln + 190lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-19ln' to each side of the equation. 160 + -19ln = 46 + 19ln + -19ln + 190lnt Combine like terms: 19ln + -19ln = 0 160 + -19ln = 46 + 0 + 190lnt 160 + -19ln = 46 + 190lnt Add '-190lnt' to each side of the equation. 160 + -19ln + -190lnt = 46 + 190lnt + -190lnt Combine like terms: 190lnt + -190lnt = 0 160 + -19ln + -190lnt = 46 + 0 160 + -19ln + -190lnt = 46 Add '-160' to each side of the equation. 160 + -19ln + -160 + -190lnt = 46 + -160 Reorder the terms: 160 + -160 + -19ln + -190lnt = 46 + -160 Combine like terms: 160 + -160 = 0 0 + -19ln + -190lnt = 46 + -160 -19ln + -190lnt = 46 + -160 Combine like terms: 46 + -160 = -114 -19ln + -190lnt = -114 Reorder the terms: 114 + -19ln + -190lnt = -114 + 114 Combine like terms: -114 + 114 = 0 114 + -19ln + -190lnt = 0 Factor out the Greatest Common Factor (GCF), '19'. 19(6 + -1ln + -10lnt) = 0 Ignore the factor 19.Subproblem 1
Set the factor '(6 + -1ln + -10lnt)' equal to zero and attempt to solve: Simplifying 6 + -1ln + -10lnt = 0 Solving 6 + -1ln + -10lnt = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -1ln + -6 + -10lnt = 0 + -6 Reorder the terms: 6 + -6 + -1ln + -10lnt = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1ln + -10lnt = 0 + -6 -1ln + -10lnt = 0 + -6 Combine like terms: 0 + -6 = -6 -1ln + -10lnt = -6 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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