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