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Simplifying ln(3x + -1) = ln(9 + -1x * x) Reorder the terms: ln(-1 + 3x) = ln(9 + -1x * x) (-1 * ln + 3x * ln) = ln(9 + -1x * x) (-1ln + 3lnx) = ln(9 + -1x * x) Multiply x * x -1ln + 3lnx = ln(9 + -1x2) -1ln + 3lnx = (9 * ln + -1x2 * ln) -1ln + 3lnx = (9ln + -1lnx2) Solving -1ln + 3lnx = 9ln + -1lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -1ln + -9ln + 3lnx = 9ln + -9ln + -1lnx2 Combine like terms: -1ln + -9ln = -10ln -10ln + 3lnx = 9ln + -9ln + -1lnx2 Combine like terms: 9ln + -9ln = 0 -10ln + 3lnx = 0 + -1lnx2 -10ln + 3lnx = -1lnx2 Add 'lnx2' to each side of the equation. -10ln + 3lnx + lnx2 = -1lnx2 + lnx2 Combine like terms: -1lnx2 + lnx2 = 0 -10ln + 3lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-10 + 3x + x2) = 0 Factor a trinomial. ln((-5 + -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 '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Add 'x' to each side of the equation. -1x + x = 5 + x Combine like terms: -1x + x = 0 0 = 5 + x Simplifying 0 = 5 + 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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