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Simplifying 0.4ln(4000 + -1x) + 0.6ln(200 + -1x) = ln(1000) (4000 * 0.4ln + -1x * 0.4ln) + 0.6ln(200 + -1x) = ln(1000) (1600ln + -0.4lnx) + 0.6ln(200 + -1x) = ln(1000) 1600ln + -0.4lnx + (200 * 0.6ln + -1x * 0.6ln) = ln(1000) 1600ln + -0.4lnx + (120ln + -0.6lnx) = ln(1000) Reorder the terms: 1600ln + 120ln + -0.4lnx + -0.6lnx = ln(1000) Combine like terms: 1600ln + 120ln = 1720ln 1720ln + -0.4lnx + -0.6lnx = ln(1000) Combine like terms: -0.4lnx + -0.6lnx = -1lnx 1720ln + -1lnx = ln(1000) Reorder the terms for easier multiplication: 1720ln + -1lnx = 1000ln Solving 1720ln + -1lnx = 1000ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1000ln' to each side of the equation. 1720ln + -1000ln + -1lnx = 1000ln + -1000ln Combine like terms: 1720ln + -1000ln = 720ln 720ln + -1lnx = 1000ln + -1000ln Combine like terms: 1000ln + -1000ln = 0 720ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(720 + -1x) = 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 '(720 + -1x)' equal to zero and attempt to solve: Simplifying 720 + -1x = 0 Solving 720 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-720' to each side of the equation. 720 + -720 + -1x = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -1x = 0 + -720 -1x = 0 + -720 Combine like terms: 0 + -720 = -720 -1x = -720 Add 'x' to each side of the equation. -1x + x = -720 + x Combine like terms: -1x + x = 0 0 = -720 + x Simplifying 0 = -720 + x 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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