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Simplifying ln(x + -5) = ln(x + 5) + -1ln(x + -7) Reorder the terms: ln(-5 + x) = ln(x + 5) + -1ln(x + -7) (-5 * ln + x * ln) = ln(x + 5) + -1ln(x + -7) (-5ln + lnx) = ln(x + 5) + -1ln(x + -7) Reorder the terms: -5ln + lnx = ln(5 + x) + -1ln(x + -7) -5ln + lnx = (5 * ln + x * ln) + -1ln(x + -7) -5ln + lnx = (5ln + lnx) + -1ln(x + -7) Reorder the terms: -5ln + lnx = 5ln + lnx + -1ln(-7 + x) -5ln + lnx = 5ln + lnx + (-7 * -1ln + x * -1ln) -5ln + lnx = 5ln + lnx + (7ln + -1lnx) Reorder the terms: -5ln + lnx = 5ln + 7ln + lnx + -1lnx Combine like terms: 5ln + 7ln = 12ln -5ln + lnx = 12ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5ln + lnx = 12ln + 0 -5ln + lnx = 12ln Solving -5ln + 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. -5ln + -12ln + lnx = 12ln + -12ln Combine like terms: -5ln + -12ln = -17ln -17ln + lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -17ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-17 + 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 '(-17 + x)' equal to zero and attempt to solve: Simplifying -17 + x = 0 Solving -17 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + x = 0 + 17 x = 0 + 17 Combine like terms: 0 + 17 = 17 x = 17 Add '-1x' to each side of the equation. x + -1x = 17 + -1x Combine like terms: x + -1x = 0 0 = 17 + -1x Simplifying 0 = 17 + -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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