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Simplifying ln(x) = ln(x2 + -56) Multiply ln * x lnx = ln(x2 + -56) Reorder the terms: lnx = ln(-56 + x2) lnx = (-56 * ln + x2 * ln) lnx = (-56ln + lnx2) Solving lnx = -56ln + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '56ln' to each side of the equation. 56ln + lnx = -56ln + 56ln + lnx2 Combine like terms: -56ln + 56ln = 0 56ln + lnx = 0 + lnx2 56ln + lnx = lnx2 Add '-1lnx2' to each side of the equation. 56ln + lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 56ln + lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(56 + x + -1x2) = 0 Factor a trinomial. ln((8 + -1x)(7 + 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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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 '(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. The solution to this equation could not be determined.
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