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Simplifying ln(x + 7) = ln(x + -6) + -1ln(x + 6) Reorder the terms: ln(7 + x) = ln(x + -6) + -1ln(x + 6) (7 * ln + x * ln) = ln(x + -6) + -1ln(x + 6) (7ln + lnx) = ln(x + -6) + -1ln(x + 6) Reorder the terms: 7ln + lnx = ln(-6 + x) + -1ln(x + 6) 7ln + lnx = (-6 * ln + x * ln) + -1ln(x + 6) 7ln + lnx = (-6ln + lnx) + -1ln(x + 6) Reorder the terms: 7ln + lnx = -6ln + lnx + -1ln(6 + x) 7ln + lnx = -6ln + lnx + (6 * -1ln + x * -1ln) 7ln + lnx = -6ln + lnx + (-6ln + -1lnx) Reorder the terms: 7ln + lnx = -6ln + -6ln + lnx + -1lnx Combine like terms: -6ln + -6ln = -12ln 7ln + lnx = -12ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 7ln + lnx = -12ln + 0 7ln + lnx = -12ln Solving 7ln + lnx = -12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 7ln + 12ln + lnx = -12ln + 12ln Combine like terms: 7ln + 12ln = 19ln 19ln + lnx = -12ln + 12ln Combine like terms: -12ln + 12ln = 0 19ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(19 + 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 '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Add '-1x' to each side of the equation. x + -1x = -19 + -1x Combine like terms: x + -1x = 0 0 = -19 + -1x Simplifying 0 = -19 + -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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