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