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Simplifying 400 + 50ln(90t + 1) = 0.05(12300 + 1000ln(t + 1)) Reorder the terms: 400 + 50ln(1 + 90t) = 0.05(12300 + 1000ln(t + 1)) 400 + (1 * 50ln + 90t * 50ln) = 0.05(12300 + 1000ln(t + 1)) 400 + (50ln + 4500lnt) = 0.05(12300 + 1000ln(t + 1)) Reorder the terms: 400 + 50ln + 4500lnt = 0.05(12300 + 1000ln(1 + t)) 400 + 50ln + 4500lnt = 0.05(12300 + (1 * 1000ln + t * 1000ln)) 400 + 50ln + 4500lnt = 0.05(12300 + (1000ln + 1000lnt)) 400 + 50ln + 4500lnt = (12300 * 0.05 + 1000ln * 0.05 + 1000lnt * 0.05) 400 + 50ln + 4500lnt = (615 + 50ln + 50lnt) Add '-50ln' to each side of the equation. 400 + 50ln + -50ln + 4500lnt = 615 + 50ln + -50ln + 50lnt Combine like terms: 50ln + -50ln = 0 400 + 0 + 4500lnt = 615 + 50ln + -50ln + 50lnt 400 + 4500lnt = 615 + 50ln + -50ln + 50lnt Combine like terms: 50ln + -50ln = 0 400 + 4500lnt = 615 + 0 + 50lnt 400 + 4500lnt = 615 + 50lnt Solving 400 + 4500lnt = 615 + 50lnt Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-50lnt' to each side of the equation. 400 + 4500lnt + -50lnt = 615 + 50lnt + -50lnt Combine like terms: 4500lnt + -50lnt = 4450lnt 400 + 4450lnt = 615 + 50lnt + -50lnt Combine like terms: 50lnt + -50lnt = 0 400 + 4450lnt = 615 + 0 400 + 4450lnt = 615 Add '-400' to each side of the equation. 400 + -400 + 4450lnt = 615 + -400 Combine like terms: 400 + -400 = 0 0 + 4450lnt = 615 + -400 4450lnt = 615 + -400 Combine like terms: 615 + -400 = 215 4450lnt = 215 Divide each side by '4450nt'. l = 0.04831460674n-1t-1 Simplifying l = 0.04831460674n-1t-1
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