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