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Simplifying 0 = ln(x2 + 3x + 5) Reorder the terms: 0 = ln(5 + 3x + x2) 0 = (5 * ln + 3x * ln + x2 * ln) 0 = (5ln + 3lnx + lnx2) Solving 0 = 5ln + 3lnx + lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 0 + -5ln = 5ln + 3lnx + -5ln + lnx2 Remove the zero: -5ln = 5ln + 3lnx + -5ln + lnx2 Reorder the terms: -5ln = 5ln + -5ln + 3lnx + lnx2 Combine like terms: 5ln + -5ln = 0 -5ln = 0 + 3lnx + lnx2 -5ln = 3lnx + lnx2 Add '-3lnx' to each side of the equation. -5ln + -3lnx = 3lnx + -3lnx + lnx2 Combine like terms: 3lnx + -3lnx = 0 -5ln + -3lnx = 0 + lnx2 -5ln + -3lnx = lnx2 Add '-1lnx2' to each side of the equation. -5ln + -3lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -5ln + -3lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 3x + x2) = 0 Ignore the factor -1.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 '(5 + 3x + x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + x2 = 0 Solving 5 + 3x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 3x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 3x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x + x2 = 0 + -5 3x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 3x + x2 = -5 Add '-3x' to each side of the equation. 3x + -3x + x2 = -5 + -3x Combine like terms: 3x + -3x = 0 0 + x2 = -5 + -3x x2 = -5 + -3x Add '-1x2' to each side of the equation. x2 + -1x2 = -5 + -3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -5 + -3x + -1x2 Simplifying 0 = -5 + -3x + -1x2 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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