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