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Simplifying ln(x + -1) = ln(x + -9) + -1ln(x + 6) Reorder the terms: ln(-1 + x) = ln(x + -9) + -1ln(x + 6) (-1 * ln + x * ln) = ln(x + -9) + -1ln(x + 6) (-1ln + lnx) = ln(x + -9) + -1ln(x + 6) Reorder the terms: -1ln + lnx = ln(-9 + x) + -1ln(x + 6) -1ln + lnx = (-9 * ln + x * ln) + -1ln(x + 6) -1ln + lnx = (-9ln + lnx) + -1ln(x + 6) Reorder the terms: -1ln + lnx = -9ln + lnx + -1ln(6 + x) -1ln + lnx = -9ln + lnx + (6 * -1ln + x * -1ln) -1ln + lnx = -9ln + lnx + (-6ln + -1lnx) Reorder the terms: -1ln + lnx = -9ln + -6ln + lnx + -1lnx Combine like terms: -9ln + -6ln = -15ln -1ln + lnx = -15ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1ln + lnx = -15ln + 0 -1ln + lnx = -15ln Solving -1ln + lnx = -15ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '15ln' to each side of the equation. -1ln + 15ln + lnx = -15ln + 15ln Combine like terms: -1ln + 15ln = 14ln 14ln + lnx = -15ln + 15ln Combine like terms: -15ln + 15ln = 0 14ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(14 + 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 '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Add '-1x' to each side of the equation. x + -1x = -14 + -1x Combine like terms: x + -1x = 0 0 = -14 + -1x Simplifying 0 = -14 + -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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