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Simplifying ln(60 + -2x) = ln(x2 + -6x) (60 * ln + -2x * ln) = ln(x2 + -6x) (60ln + -2lnx) = ln(x2 + -6x) Reorder the terms: 60ln + -2lnx = ln(-6x + x2) 60ln + -2lnx = (-6x * ln + x2 * ln) 60ln + -2lnx = (-6lnx + lnx2) Solving 60ln + -2lnx = -6lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6lnx' to each side of the equation. 60ln + -2lnx + 6lnx = -6lnx + 6lnx + lnx2 Combine like terms: -2lnx + 6lnx = 4lnx 60ln + 4lnx = -6lnx + 6lnx + lnx2 Combine like terms: -6lnx + 6lnx = 0 60ln + 4lnx = 0 + lnx2 60ln + 4lnx = lnx2 Add '-1lnx2' to each side of the equation. 60ln + 4lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 60ln + 4lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(60 + 4x + -1x2) = 0 Factor a trinomial. ln((10 + -1x)(6 + 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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + 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 '(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. The solution to this equation could not be determined.
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