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Simplifying ln(40 + -2x) = ln(x2 + 4x) (40 * ln + -2x * ln) = ln(x2 + 4x) (40ln + -2lnx) = ln(x2 + 4x) Reorder the terms: 40ln + -2lnx = ln(4x + x2) 40ln + -2lnx = (4x * ln + x2 * ln) 40ln + -2lnx = (4lnx + lnx2) Solving 40ln + -2lnx = 4lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. 40ln + -2lnx + -4lnx = 4lnx + -4lnx + lnx2 Combine like terms: -2lnx + -4lnx = -6lnx 40ln + -6lnx = 4lnx + -4lnx + lnx2 Combine like terms: 4lnx + -4lnx = 0 40ln + -6lnx = 0 + lnx2 40ln + -6lnx = lnx2 Add '-1lnx2' to each side of the equation. 40ln + -6lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 40ln + -6lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(40 + -6x + -1x2) = 0 Factor a trinomial. ln((4 + -1x)(10 + 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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 '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 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 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Add '-1x' to each side of the equation. x + -1x = -10 + -1x Combine like terms: x + -1x = 0 0 = -10 + -1x Simplifying 0 = -10 + -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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