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Simplifying [0.2ln(580 + -1Y)] + [0.8ln(180 + -1Y)] = ln(200) [(580 * 0.2ln + -1Y * 0.2ln)] + [0.8ln(180 + -1Y)] = ln(200) [(116ln + -0.2lnY)] + [0.8ln(180 + -1Y)] = ln(200) [116ln + -0.2lnY] + [0.8ln(180 + -1Y)] = ln(200) Remove brackets around [116ln + -0.2lnY] 116ln + -0.2lnY + [0.8ln(180 + -1Y)] = ln(200) 116ln + -0.2lnY + [(180 * 0.8ln + -1Y * 0.8ln)] = ln(200) 116ln + -0.2lnY + [(144ln + -0.8lnY)] = ln(200) 116ln + -0.2lnY + [144ln + -0.8lnY] = ln(200) Remove brackets around [144ln + -0.8lnY] 116ln + -0.2lnY + 144ln + -0.8lnY = ln(200) Reorder the terms: 116ln + 144ln + -0.2lnY + -0.8lnY = ln(200) Combine like terms: 116ln + 144ln = 260ln 260ln + -0.2lnY + -0.8lnY = ln(200) Combine like terms: -0.2lnY + -0.8lnY = -1lnY 260ln + -1lnY = ln(200) Reorder the terms for easier multiplication: 260ln + -1lnY = 200ln Solving 260ln + -1lnY = 200ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-200ln' to each side of the equation. 260ln + -200ln + -1lnY = 200ln + -200ln Combine like terms: 260ln + -200ln = 60ln 60ln + -1lnY = 200ln + -200ln Combine like terms: 200ln + -200ln = 0 60ln + -1lnY = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(60 + -1Y) = 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 '(60 + -1Y)' equal to zero and attempt to solve: Simplifying 60 + -1Y = 0 Solving 60 + -1Y = 0 Move all terms containing l to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1Y = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1Y = 0 + -60 -1Y = 0 + -60 Combine like terms: 0 + -60 = -60 -1Y = -60 Add 'Y' to each side of the equation. -1Y + Y = -60 + Y Combine like terms: -1Y + Y = 0 0 = -60 + Y Simplifying 0 = -60 + Y 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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