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Simplifying 500 = 20 + 150ln(8t + 1) Reorder the terms: 500 = 20 + 150ln(1 + 8t) 500 = 20 + (1 * 150ln + 8t * 150ln) 500 = 20 + (150ln + 1200lnt) Solving 500 = 20 + 150ln + 1200lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-150ln' to each side of the equation. 500 + -150ln = 20 + 150ln + -150ln + 1200lnt Combine like terms: 150ln + -150ln = 0 500 + -150ln = 20 + 0 + 1200lnt 500 + -150ln = 20 + 1200lnt Add '-1200lnt' to each side of the equation. 500 + -150ln + -1200lnt = 20 + 1200lnt + -1200lnt Combine like terms: 1200lnt + -1200lnt = 0 500 + -150ln + -1200lnt = 20 + 0 500 + -150ln + -1200lnt = 20 Add '-500' to each side of the equation. 500 + -150ln + -500 + -1200lnt = 20 + -500 Reorder the terms: 500 + -500 + -150ln + -1200lnt = 20 + -500 Combine like terms: 500 + -500 = 0 0 + -150ln + -1200lnt = 20 + -500 -150ln + -1200lnt = 20 + -500 Combine like terms: 20 + -500 = -480 -150ln + -1200lnt = -480 Reorder the terms: 480 + -150ln + -1200lnt = -480 + 480 Combine like terms: -480 + 480 = 0 480 + -150ln + -1200lnt = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(16 + -5ln + -40lnt) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(16 + -5ln + -40lnt)' equal to zero and attempt to solve: Simplifying 16 + -5ln + -40lnt = 0 Solving 16 + -5ln + -40lnt = 0 Move all terms containing l to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -5ln + -16 + -40lnt = 0 + -16 Reorder the terms: 16 + -16 + -5ln + -40lnt = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -5ln + -40lnt = 0 + -16 -5ln + -40lnt = 0 + -16 Combine like terms: 0 + -16 = -16 -5ln + -40lnt = -16 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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