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Simplifying ln(x + -2) + ln(2x + 5) = ln(x2 + 5x + -5) Reorder the terms: ln(-2 + x) + ln(2x + 5) = ln(x2 + 5x + -5) (-2 * ln + x * ln) + ln(2x + 5) = ln(x2 + 5x + -5) (-2ln + lnx) + ln(2x + 5) = ln(x2 + 5x + -5) Reorder the terms: -2ln + lnx + ln(5 + 2x) = ln(x2 + 5x + -5) -2ln + lnx + (5 * ln + 2x * ln) = ln(x2 + 5x + -5) -2ln + lnx + (5ln + 2lnx) = ln(x2 + 5x + -5) Reorder the terms: -2ln + 5ln + lnx + 2lnx = ln(x2 + 5x + -5) Combine like terms: -2ln + 5ln = 3ln 3ln + lnx + 2lnx = ln(x2 + 5x + -5) Combine like terms: lnx + 2lnx = 3lnx 3ln + 3lnx = ln(x2 + 5x + -5) Reorder the terms: 3ln + 3lnx = ln(-5 + 5x + x2) 3ln + 3lnx = (-5 * ln + 5x * ln + x2 * ln) 3ln + 3lnx = (-5ln + 5lnx + lnx2) Solving 3ln + 3lnx = -5ln + 5lnx + lnx2 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. 3ln + 5ln + 3lnx = -5ln + 5lnx + 5ln + lnx2 Combine like terms: 3ln + 5ln = 8ln 8ln + 3lnx = -5ln + 5lnx + 5ln + lnx2 Reorder the terms: 8ln + 3lnx = -5ln + 5ln + 5lnx + lnx2 Combine like terms: -5ln + 5ln = 0 8ln + 3lnx = 0 + 5lnx + lnx2 8ln + 3lnx = 5lnx + lnx2 Add '-5lnx' to each side of the equation. 8ln + 3lnx + -5lnx = 5lnx + -5lnx + lnx2 Combine like terms: 3lnx + -5lnx = -2lnx 8ln + -2lnx = 5lnx + -5lnx + lnx2 Combine like terms: 5lnx + -5lnx = 0 8ln + -2lnx = 0 + lnx2 8ln + -2lnx = lnx2 Add '-1lnx2' to each side of the equation. 8ln + -2lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 8ln + -2lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -2x + -1x2) = 0 Factor a trinomial. ln((2 + -1x)(4 + x)) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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