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Simplifying ln(x + -1) + ln(2 + -1x) = ln(2x + -3) Reorder the terms: ln(-1 + x) + ln(2 + -1x) = ln(2x + -3) (-1 * ln + x * ln) + ln(2 + -1x) = ln(2x + -3) (-1ln + lnx) + ln(2 + -1x) = ln(2x + -3) -1ln + lnx + (2 * ln + -1x * ln) = ln(2x + -3) -1ln + lnx + (2ln + -1lnx) = ln(2x + -3) Reorder the terms: -1ln + 2ln + lnx + -1lnx = ln(2x + -3) Combine like terms: -1ln + 2ln = 1ln 1ln + lnx + -1lnx = ln(2x + -3) Combine like terms: lnx + -1lnx = 0 1ln + 0 = ln(2x + -3) 1ln = ln(2x + -3) Reorder the terms: 1ln = ln(-3 + 2x) 1ln = (-3 * ln + 2x * ln) 1ln = (-3ln + 2lnx) Solving 1ln = -3ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '3ln' to each side of the equation. 1ln + 3ln = -3ln + 3ln + 2lnx Combine like terms: 1ln + 3ln = 4ln 4ln = -3ln + 3ln + 2lnx Combine like terms: -3ln + 3ln = 0 4ln = 0 + 2lnx 4ln = 2lnx Add '-2lnx' to each side of the equation. 4ln + -2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 4ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(2 + -1x) = 0 Ignore the factor 2.Subproblem 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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