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Simplifying ln(x + 3) + ln(x + -3) + -3ln(x2 + 3) = 0 Reorder the terms: ln(3 + x) + ln(x + -3) + -3ln(x2 + 3) = 0 (3 * ln + x * ln) + ln(x + -3) + -3ln(x2 + 3) = 0 (3ln + lnx) + ln(x + -3) + -3ln(x2 + 3) = 0 Reorder the terms: 3ln + lnx + ln(-3 + x) + -3ln(x2 + 3) = 0 3ln + lnx + (-3 * ln + x * ln) + -3ln(x2 + 3) = 0 3ln + lnx + (-3ln + lnx) + -3ln(x2 + 3) = 0 Reorder the terms: 3ln + lnx + -3ln + lnx + -3ln(3 + x2) = 0 3ln + lnx + -3ln + lnx + (3 * -3ln + x2 * -3ln) = 0 3ln + lnx + -3ln + lnx + (-9ln + -3lnx2) = 0 Reorder the terms: 3ln + -3ln + -9ln + lnx + lnx + -3lnx2 = 0 Combine like terms: 3ln + -3ln = 0 0 + -9ln + lnx + lnx + -3lnx2 = 0 -9ln + lnx + lnx + -3lnx2 = 0 Combine like terms: lnx + lnx = 2lnx -9ln + 2lnx + -3lnx2 = 0 Solving -9ln + 2lnx + -3lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-9 + 2x + -3x2) = 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 '(-9 + 2x + -3x2)' equal to zero and attempt to solve: Simplifying -9 + 2x + -3x2 = 0 Solving -9 + 2x + -3x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 2x + 9 + -3x2 = 0 + 9 Reorder the terms: -9 + 9 + 2x + -3x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x + -3x2 = 0 + 9 2x + -3x2 = 0 + 9 Combine like terms: 0 + 9 = 9 2x + -3x2 = 9 Add '-2x' to each side of the equation. 2x + -2x + -3x2 = 9 + -2x Combine like terms: 2x + -2x = 0 0 + -3x2 = 9 + -2x -3x2 = 9 + -2x Add '3x2' to each side of the equation. -3x2 + 3x2 = 9 + -2x + 3x2 Combine like terms: -3x2 + 3x2 = 0 0 = 9 + -2x + 3x2 Simplifying 0 = 9 + -2x + 3x2 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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