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Simplifying ln(x2 + -5x + 6) = ln(x + -2) + ln(x + -3) Reorder the terms: ln(6 + -5x + x2) = ln(x + -2) + ln(x + -3) (6 * ln + -5x * ln + x2 * ln) = ln(x + -2) + ln(x + -3) (6ln + -5lnx + lnx2) = ln(x + -2) + ln(x + -3) Reorder the terms: 6ln + -5lnx + lnx2 = ln(-2 + x) + ln(x + -3) 6ln + -5lnx + lnx2 = (-2 * ln + x * ln) + ln(x + -3) 6ln + -5lnx + lnx2 = (-2ln + lnx) + ln(x + -3) Reorder the terms: 6ln + -5lnx + lnx2 = -2ln + lnx + ln(-3 + x) 6ln + -5lnx + lnx2 = -2ln + lnx + (-3 * ln + x * ln) 6ln + -5lnx + lnx2 = -2ln + lnx + (-3ln + lnx) Reorder the terms: 6ln + -5lnx + lnx2 = -2ln + -3ln + lnx + lnx Combine like terms: -2ln + -3ln = -5ln 6ln + -5lnx + lnx2 = -5ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 6ln + -5lnx + lnx2 = -5ln + 2lnx Solving 6ln + -5lnx + lnx2 = -5ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 6ln + -5lnx + 5ln + lnx2 = -5ln + 5ln + 2lnx Reorder the terms: 6ln + 5ln + -5lnx + lnx2 = -5ln + 5ln + 2lnx Combine like terms: 6ln + 5ln = 11ln 11ln + -5lnx + lnx2 = -5ln + 5ln + 2lnx Combine like terms: -5ln + 5ln = 0 11ln + -5lnx + lnx2 = 0 + 2lnx 11ln + -5lnx + lnx2 = 2lnx Add '-2lnx' to each side of the equation. 11ln + -5lnx + -2lnx + lnx2 = 2lnx + -2lnx Combine like terms: -5lnx + -2lnx = -7lnx 11ln + -7lnx + lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 11ln + -7lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + -7x + x2) = 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 '(11 + -7x + x2)' equal to zero and attempt to solve: Simplifying 11 + -7x + x2 = 0 Solving 11 + -7x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -7x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -7x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7x + x2 = 0 + -11 -7x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -7x + x2 = -11 Add '7x' to each side of the equation. -7x + 7x + x2 = -11 + 7x Combine like terms: -7x + 7x = 0 0 + x2 = -11 + 7x x2 = -11 + 7x Add '-1x2' to each side of the equation. x2 + -1x2 = -11 + 7x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -11 + 7x + -1x2 Simplifying 0 = -11 + 7x + -1x2 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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