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Simplifying ln(x2 + 13) = ln(5x + 7) Reorder the terms: ln(13 + x2) = ln(5x + 7) (13 * ln + x2 * ln) = ln(5x + 7) (13ln + lnx2) = ln(5x + 7) Reorder the terms: 13ln + lnx2 = ln(7 + 5x) 13ln + lnx2 = (7 * ln + 5x * ln) 13ln + lnx2 = (7ln + 5lnx) Solving 13ln + lnx2 = 7ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-7ln' to each side of the equation. 13ln + -7ln + lnx2 = 7ln + -7ln + 5lnx Combine like terms: 13ln + -7ln = 6ln 6ln + lnx2 = 7ln + -7ln + 5lnx Combine like terms: 7ln + -7ln = 0 6ln + lnx2 = 0 + 5lnx 6ln + lnx2 = 5lnx Add '-5lnx' to each side of the equation. 6ln + -5lnx + lnx2 = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 6ln + -5lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + -5x + x2) = 0 Factor a trinomial. ln((2 + -1x)(3 + -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 '(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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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