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Simplifying ln(30 + -2x) = ln(x2 + -1x) (30 * ln + -2x * ln) = ln(x2 + -1x) (30ln + -2lnx) = ln(x2 + -1x) Reorder the terms: 30ln + -2lnx = ln(-1x + x2) 30ln + -2lnx = (-1x * ln + x2 * ln) 30ln + -2lnx = (-1lnx + lnx2) Solving 30ln + -2lnx = -1lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'lnx' to each side of the equation. 30ln + -2lnx + lnx = -1lnx + lnx + lnx2 Combine like terms: -2lnx + lnx = -1lnx 30ln + -1lnx = -1lnx + lnx + lnx2 Combine like terms: -1lnx + lnx = 0 30ln + -1lnx = 0 + lnx2 30ln + -1lnx = lnx2 Add '-1lnx2' to each side of the equation. 30ln + -1lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 30ln + -1lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(30 + -1x + -1x2) = 0 Factor a trinomial. ln((5 + -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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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