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Simplifying ln(x + 5) = ln(x + -1) + -1ln(x + 1) Reorder the terms: ln(5 + x) = ln(x + -1) + -1ln(x + 1) (5 * ln + x * ln) = ln(x + -1) + -1ln(x + 1) (5ln + lnx) = ln(x + -1) + -1ln(x + 1) Reorder the terms: 5ln + lnx = ln(-1 + x) + -1ln(x + 1) 5ln + lnx = (-1 * ln + x * ln) + -1ln(x + 1) 5ln + lnx = (-1ln + lnx) + -1ln(x + 1) Reorder the terms: 5ln + lnx = -1ln + lnx + -1ln(1 + x) 5ln + lnx = -1ln + lnx + (1 * -1ln + x * -1ln) 5ln + lnx = -1ln + lnx + (-1ln + -1lnx) Reorder the terms: 5ln + lnx = -1ln + -1ln + lnx + -1lnx Combine like terms: -1ln + -1ln = -2ln 5ln + lnx = -2ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 5ln + lnx = -2ln + 0 5ln + lnx = -2ln Solving 5ln + lnx = -2ln 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. 5ln + 2ln + lnx = -2ln + 2ln Combine like terms: 5ln + 2ln = 7ln 7ln + lnx = -2ln + 2ln Combine like terms: -2ln + 2ln = 0 7ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -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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