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Simplifying ln(x + 1) + -1ln(x + -1) = ln(x + 5) Reorder the terms: ln(1 + x) + -1ln(x + -1) = ln(x + 5) (1 * ln + x * ln) + -1ln(x + -1) = ln(x + 5) (1ln + lnx) + -1ln(x + -1) = ln(x + 5) Reorder the terms: 1ln + lnx + -1ln(-1 + x) = ln(x + 5) 1ln + lnx + (-1 * -1ln + x * -1ln) = ln(x + 5) 1ln + lnx + (1ln + -1lnx) = ln(x + 5) Reorder the terms: 1ln + 1ln + lnx + -1lnx = ln(x + 5) Combine like terms: 1ln + 1ln = 2ln 2ln + lnx + -1lnx = ln(x + 5) Combine like terms: lnx + -1lnx = 0 2ln + 0 = ln(x + 5) 2ln = ln(x + 5) Reorder the terms: 2ln = ln(5 + x) 2ln = (5 * ln + x * ln) 2ln = (5ln + lnx) Solving 2ln = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. 2ln + -5ln = 5ln + -5ln + lnx Combine like terms: 2ln + -5ln = -3ln -3ln = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -3ln = 0 + lnx -3ln = lnx Add '-1lnx' to each side of the equation. -3ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(3 + x) = 0 Ignore the factor -1.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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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