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Simplifying 2ln(x + 8) + ln(x) = ln(12x2 + 89x + 100) Reorder the terms: 2ln(8 + x) + ln(x) = ln(12x2 + 89x + 100) (8 * 2ln + x * 2ln) + ln(x) = ln(12x2 + 89x + 100) (16ln + 2lnx) + ln(x) = ln(12x2 + 89x + 100) Multiply ln * x 16ln + 2lnx + lnx = ln(12x2 + 89x + 100) Combine like terms: 2lnx + lnx = 3lnx 16ln + 3lnx = ln(12x2 + 89x + 100) Reorder the terms: 16ln + 3lnx = ln(100 + 89x + 12x2) 16ln + 3lnx = (100 * ln + 89x * ln + 12x2 * ln) 16ln + 3lnx = (100ln + 89lnx + 12lnx2) Solving 16ln + 3lnx = 100ln + 89lnx + 12lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-100ln' to each side of the equation. 16ln + -100ln + 3lnx = 100ln + 89lnx + -100ln + 12lnx2 Combine like terms: 16ln + -100ln = -84ln -84ln + 3lnx = 100ln + 89lnx + -100ln + 12lnx2 Reorder the terms: -84ln + 3lnx = 100ln + -100ln + 89lnx + 12lnx2 Combine like terms: 100ln + -100ln = 0 -84ln + 3lnx = 0 + 89lnx + 12lnx2 -84ln + 3lnx = 89lnx + 12lnx2 Add '-89lnx' to each side of the equation. -84ln + 3lnx + -89lnx = 89lnx + -89lnx + 12lnx2 Combine like terms: 3lnx + -89lnx = -86lnx -84ln + -86lnx = 89lnx + -89lnx + 12lnx2 Combine like terms: 89lnx + -89lnx = 0 -84ln + -86lnx = 0 + 12lnx2 -84ln + -86lnx = 12lnx2 Add '-12lnx2' to each side of the equation. -84ln + -86lnx + -12lnx2 = 12lnx2 + -12lnx2 Combine like terms: 12lnx2 + -12lnx2 = 0 -84ln + -86lnx + -12lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(42 + 43x + 6x2) = 0 Factor a trinomial. -2ln((6 + x)(7 + 6x)) = 0 Ignore the factor -2.Subproblem 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 '(7 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Add '-6x' to each side of the equation. 6x + -6x = -7 + -6x Combine like terms: 6x + -6x = 0 0 = -7 + -6x Simplifying 0 = -7 + -6x 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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