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Simplifying 0 = 3ln(x + 1) + -2ln(x + -4) Reorder the terms: 0 = 3ln(1 + x) + -2ln(x + -4) 0 = (1 * 3ln + x * 3ln) + -2ln(x + -4) 0 = (3ln + 3lnx) + -2ln(x + -4) Reorder the terms: 0 = 3ln + 3lnx + -2ln(-4 + x) 0 = 3ln + 3lnx + (-4 * -2ln + x * -2ln) 0 = 3ln + 3lnx + (8ln + -2lnx) Reorder the terms: 0 = 3ln + 8ln + 3lnx + -2lnx Combine like terms: 3ln + 8ln = 11ln 0 = 11ln + 3lnx + -2lnx Combine like terms: 3lnx + -2lnx = 1lnx 0 = 11ln + 1lnx Solving 0 = 11ln + 1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. 0 + -11ln = 11ln + -11ln + 1lnx Remove the zero: -11ln = 11ln + -11ln + 1lnx Combine like terms: 11ln + -11ln = 0 -11ln = 0 + 1lnx -11ln = 1lnx Add '-1lnx' to each side of the equation. -11ln + -1lnx = 1lnx + -1lnx Combine like terms: 1lnx + -1lnx = 0 -11ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(11 + x) = 0 Ignore the factor -1.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 '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Add '-1x' to each side of the equation. x + -1x = -11 + -1x Combine like terms: x + -1x = 0 0 = -11 + -1x Simplifying 0 = -11 + -1x 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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