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Simplifying ln(0.8x + 1) = ln(0.8y + 1) + -1ln(1 + -1u) Reorder the terms: ln(1 + 0.8x) = ln(0.8y + 1) + -1ln(1 + -1u) (1 * ln + 0.8x * ln) = ln(0.8y + 1) + -1ln(1 + -1u) (1ln + 0.8lnx) = ln(0.8y + 1) + -1ln(1 + -1u) Reorder the terms: 1ln + 0.8lnx = ln(1 + 0.8y) + -1ln(1 + -1u) 1ln + 0.8lnx = (1 * ln + 0.8y * ln) + -1ln(1 + -1u) 1ln + 0.8lnx = (1ln + 0.8lny) + -1ln(1 + -1u) 1ln + 0.8lnx = 1ln + 0.8lny + (1 * -1ln + -1u * -1ln) 1ln + 0.8lnx = 1ln + 0.8lny + (-1ln + 1lnu) Reorder the terms: 1ln + 0.8lnx = 1ln + -1ln + 1lnu + 0.8lny Combine like terms: 1ln + -1ln = 0 1ln + 0.8lnx = 0 + 1lnu + 0.8lny 1ln + 0.8lnx = 1lnu + 0.8lny Solving 1ln + 0.8lnx = 1lnu + 0.8lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnu' to each side of the equation. 1ln + -1lnu + 0.8lnx = 1lnu + -1lnu + 0.8lny Combine like terms: 1lnu + -1lnu = 0 1ln + -1lnu + 0.8lnx = 0 + 0.8lny 1ln + -1lnu + 0.8lnx = 0.8lny Add '-0.8lny' to each side of the equation. 1ln + -1lnu + 0.8lnx + -0.8lny = 0.8lny + -0.8lny Combine like terms: 0.8lny + -0.8lny = 0.0 1ln + -1lnu + 0.8lnx + -0.8lny = 0.0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1u + 0.8x + -0.8y) = 0.0Subproblem 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 '(1 + -1u + 0.8x + -0.8y)' equal to zero and attempt to solve: Simplifying 1 + -1u + 0.8x + -0.8y = 0 Solving 1 + -1u + 0.8x + -0.8y = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1u + 0.8x + -1 + -0.8y = 0 + -1 Reorder the terms: 1 + -1 + -1u + 0.8x + -0.8y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1u + 0.8x + -0.8y = 0 + -1 -1u + 0.8x + -0.8y = 0 + -1 Combine like terms: 0 + -1 = -1 -1u + 0.8x + -0.8y = -1 Add 'u' to each side of the equation. -1u + 0.8x + u + -0.8y = -1 + u Reorder the terms: -1u + u + 0.8x + -0.8y = -1 + u Combine like terms: -1u + u = 0 0 + 0.8x + -0.8y = -1 + u 0.8x + -0.8y = -1 + u Add '-0.8x' to each side of the equation. 0.8x + -0.8x + -0.8y = -1 + u + -0.8x Combine like terms: 0.8x + -0.8x = 0.0 0.0 + -0.8y = -1 + u + -0.8x -0.8y = -1 + u + -0.8x Add '0.8y' to each side of the equation. -0.8y + 0.8y = -1 + u + -0.8x + 0.8y Combine like terms: -0.8y + 0.8y = 0.0 0.0 = -1 + u + -0.8x + 0.8y Simplifying 0.0 = -1 + u + -0.8x + 0.8y 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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