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Simplifying ln(8x + 17) = ln(5 + -1x2) Reorder the terms: ln(17 + 8x) = ln(5 + -1x2) (17 * ln + 8x * ln) = ln(5 + -1x2) (17ln + 8lnx) = ln(5 + -1x2) 17ln + 8lnx = (5 * ln + -1x2 * ln) 17ln + 8lnx = (5ln + -1lnx2) Solving 17ln + 8lnx = 5ln + -1lnx2 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. 17ln + -5ln + 8lnx = 5ln + -5ln + -1lnx2 Combine like terms: 17ln + -5ln = 12ln 12ln + 8lnx = 5ln + -5ln + -1lnx2 Combine like terms: 5ln + -5ln = 0 12ln + 8lnx = 0 + -1lnx2 12ln + 8lnx = -1lnx2 Add 'lnx2' to each side of the equation. 12ln + 8lnx + lnx2 = -1lnx2 + lnx2 Combine like terms: -1lnx2 + lnx2 = 0 12ln + 8lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(12 + 8x + x2) = 0 Factor a trinomial. ln((6 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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