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