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