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Simplifying ln(x2 + 1) = ln(-9x + -13) Reorder the terms: ln(1 + x2) = ln(-9x + -13) (1 * ln + x2 * ln) = ln(-9x + -13) (1ln + lnx2) = ln(-9x + -13) Reorder the terms: 1ln + lnx2 = ln(-13 + -9x) 1ln + lnx2 = (-13 * ln + -9x * ln) 1ln + lnx2 = (-13ln + -9lnx) Solving 1ln + lnx2 = -13ln + -9lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '13ln' to each side of the equation. 1ln + 13ln + lnx2 = -13ln + 13ln + -9lnx Combine like terms: 1ln + 13ln = 14ln 14ln + lnx2 = -13ln + 13ln + -9lnx Combine like terms: -13ln + 13ln = 0 14ln + lnx2 = 0 + -9lnx 14ln + lnx2 = -9lnx Add '9lnx' to each side of the equation. 14ln + 9lnx + lnx2 = -9lnx + 9lnx Combine like terms: -9lnx + 9lnx = 0 14ln + 9lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(14 + 9x + x2) = 0 Factor a trinomial. ln((7 + x)(2 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x 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 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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