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Simplifying ln(x2 + -3x + 6) + -1ln(x + 1) = lnx Reorder the terms: ln(6 + -3x + x2) + -1ln(x + 1) = lnx (6 * ln + -3x * ln + x2 * ln) + -1ln(x + 1) = lnx (6ln + -3lnx + lnx2) + -1ln(x + 1) = lnx Reorder the terms: 6ln + -3lnx + lnx2 + -1ln(1 + x) = lnx 6ln + -3lnx + lnx2 + (1 * -1ln + x * -1ln) = lnx 6ln + -3lnx + lnx2 + (-1ln + -1lnx) = lnx Reorder the terms: 6ln + -1ln + -3lnx + -1lnx + lnx2 = lnx Combine like terms: 6ln + -1ln = 5ln 5ln + -3lnx + -1lnx + lnx2 = lnx Combine like terms: -3lnx + -1lnx = -4lnx 5ln + -4lnx + lnx2 = lnx Solving 5ln + -4lnx + lnx2 = lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lnx' to each side of the equation. 5ln + -4lnx + -1lnx + lnx2 = lnx + -1lnx Combine like terms: -4lnx + -1lnx = -5lnx 5ln + -5lnx + lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 5ln + -5lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -5x + x2) = 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 '(5 + -5x + x2)' equal to zero and attempt to solve: Simplifying 5 + -5x + x2 = 0 Solving 5 + -5x + 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 + -5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5x + x2 = 0 + -5 -5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5x + x2 = -5 Add '5x' to each side of the equation. -5x + 5x + x2 = -5 + 5x Combine like terms: -5x + 5x = 0 0 + x2 = -5 + 5x x2 = -5 + 5x Add '-1x2' to each side of the equation. x2 + -1x2 = -5 + 5x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -5 + 5x + -1x2 Simplifying 0 = -5 + 5x + -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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