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Simplifying ln((3x2) + -1) + ln(3) + -1ln(x + 5) = 0 Reorder the terms: ln(-1 + (3x2)) + ln(3) + -1ln(x + 5) = 0 (-1 * ln + (3x2) * ln) + ln(3) + -1ln(x + 5) = 0 (-1ln + 3lnx2) + ln(3) + -1ln(x + 5) = 0 Reorder the terms for easier multiplication: -1ln + 3lnx2 + 3ln + -1ln(x + 5) = 0 Reorder the terms: -1ln + 3lnx2 + 3ln + -1ln(5 + x) = 0 -1ln + 3lnx2 + 3ln + (5 * -1ln + x * -1ln) = 0 -1ln + 3lnx2 + 3ln + (-5ln + -1lnx) = 0 Reorder the terms: -1ln + 3ln + -5ln + -1lnx + 3lnx2 = 0 Combine like terms: -1ln + 3ln = 2ln 2ln + -5ln + -1lnx + 3lnx2 = 0 Combine like terms: 2ln + -5ln = -3ln -3ln + -1lnx + 3lnx2 = 0 Solving -3ln + -1lnx + 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(-3 + -1x + 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 '(-3 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -3 + -1x + 3x2 = 0 Solving -3 + -1x + 3x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1x + 3 + 3x2 = 0 + 3 Reorder the terms: -3 + 3 + -1x + 3x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x + 3x2 = 0 + 3 -1x + 3x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x + 3x2 = 3 Add 'x' to each side of the equation. -1x + x + 3x2 = 3 + x Combine like terms: -1x + x = 0 0 + 3x2 = 3 + x 3x2 = 3 + x Add '-3x2' to each side of the equation. 3x2 + -3x2 = 3 + x + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 = 3 + x + -3x2 Simplifying 0 = 3 + x + -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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