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Simplifying ln(60y + 100) + -1ln(100) = -1(ln(180x + -30) + -1ln(30)) Reorder the terms: ln(100 + 60y) + -1ln(100) = -1(ln(180x + -30) + -1ln(30)) (100 * ln + 60y * ln) + -1ln(100) = -1(ln(180x + -30) + -1ln(30)) (100ln + 60lny) + -1ln(100) = -1(ln(180x + -30) + -1ln(30)) Reorder the terms for easier multiplication: 100ln + 60lny + -1 * 100ln = -1(ln(180x + -30) + -1ln(30)) Multiply -1 * 100 100ln + 60lny + -100ln = -1(ln(180x + -30) + -1ln(30)) Reorder the terms: 100ln + -100ln + 60lny = -1(ln(180x + -30) + -1ln(30)) Combine like terms: 100ln + -100ln = 0 0 + 60lny = -1(ln(180x + -30) + -1ln(30)) 60lny = -1(ln(180x + -30) + -1ln(30)) Reorder the terms: 60lny = -1(ln(-30 + 180x) + -1ln(30)) 60lny = -1((-30 * ln + 180x * ln) + -1ln(30)) 60lny = -1((-30ln + 180lnx) + -1ln(30)) Reorder the terms for easier multiplication: 60lny = -1(-30ln + 180lnx + -1 * 30ln) Multiply -1 * 30 60lny = -1(-30ln + 180lnx + -30ln) Reorder the terms: 60lny = -1(-30ln + -30ln + 180lnx) Combine like terms: -30ln + -30ln = -60ln 60lny = -1(-60ln + 180lnx) 60lny = (-60ln * -1 + 180lnx * -1) 60lny = (60ln + -180lnx) Solving 60lny = 60ln + -180lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-60ln' to each side of the equation. -60ln + 60lny = 60ln + -60ln + -180lnx Combine like terms: 60ln + -60ln = 0 -60ln + 60lny = 0 + -180lnx -60ln + 60lny = -180lnx Add '180lnx' to each side of the equation. -60ln + 180lnx + 60lny = -180lnx + 180lnx Combine like terms: -180lnx + 180lnx = 0 -60ln + 180lnx + 60lny = 0 Factor out the Greatest Common Factor (GCF), '60ln'. 60ln(-1 + 3x + y) = 0 Ignore the factor 60.Subproblem 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 + 3x + y)' equal to zero and attempt to solve: Simplifying -1 + 3x + y = 0 Solving -1 + 3x + y = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 3x + 1 + y = 0 + 1 Reorder the terms: -1 + 1 + 3x + y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x + y = 0 + 1 3x + y = 0 + 1 Combine like terms: 0 + 1 = 1 3x + y = 1 Add '-3x' to each side of the equation. 3x + -3x + y = 1 + -3x Combine like terms: 3x + -3x = 0 0 + y = 1 + -3x y = 1 + -3x Add '-1y' to each side of the equation. y + -1y = 1 + -3x + -1y Combine like terms: y + -1y = 0 0 = 1 + -3x + -1y Simplifying 0 = 1 + -3x + -1y 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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