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Simplifying ln(x2 + x) = ln(2x + -6) Reorder the terms: ln(x + x2) = ln(2x + -6) (x * ln + x2 * ln) = ln(2x + -6) (lnx + lnx2) = ln(2x + -6) Reorder the terms: lnx + lnx2 = ln(-6 + 2x) lnx + lnx2 = (-6 * ln + 2x * ln) lnx + lnx2 = (-6ln + 2lnx) Solving lnx + lnx2 = -6ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. lnx + 6ln + lnx2 = -6ln + 6ln + 2lnx Reorder the terms: 6ln + lnx + lnx2 = -6ln + 6ln + 2lnx Combine like terms: -6ln + 6ln = 0 6ln + lnx + lnx2 = 0 + 2lnx 6ln + lnx + lnx2 = 2lnx Add '-2lnx' to each side of the equation. 6ln + lnx + -2lnx + lnx2 = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 6ln + -1lnx + lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6ln + -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + -1x + 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 '(6 + -1x + x2)' equal to zero and attempt to solve: Simplifying 6 + -1x + x2 = 0 Solving 6 + -1x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -1x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -1x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x + x2 = 0 + -6 -1x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1x + x2 = -6 Add 'x' to each side of the equation. -1x + x + x2 = -6 + x Combine like terms: -1x + x = 0 0 + x2 = -6 + x x2 = -6 + x Add '-1x2' to each side of the equation. x2 + -1x2 = -6 + x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -6 + x + -1x2 Simplifying 0 = -6 + x + -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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