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Simplifying ln(x + -5) + ln(x + 2) = ln(x + -14) Reorder the terms: ln(-5 + x) + ln(x + 2) = ln(x + -14) (-5 * ln + x * ln) + ln(x + 2) = ln(x + -14) (-5ln + lnx) + ln(x + 2) = ln(x + -14) Reorder the terms: -5ln + lnx + ln(2 + x) = ln(x + -14) -5ln + lnx + (2 * ln + x * ln) = ln(x + -14) -5ln + lnx + (2ln + lnx) = ln(x + -14) Reorder the terms: -5ln + 2ln + lnx + lnx = ln(x + -14) Combine like terms: -5ln + 2ln = -3ln -3ln + lnx + lnx = ln(x + -14) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(x + -14) Reorder the terms: -3ln + 2lnx = ln(-14 + x) -3ln + 2lnx = (-14 * ln + x * ln) -3ln + 2lnx = (-14ln + lnx) Solving -3ln + 2lnx = -14ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '14ln' to each side of the equation. -3ln + 14ln + 2lnx = -14ln + 14ln + lnx Combine like terms: -3ln + 14ln = 11ln 11ln + 2lnx = -14ln + 14ln + lnx Combine like terms: -14ln + 14ln = 0 11ln + 2lnx = 0 + lnx 11ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 11ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 11ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 11ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(11 + 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 '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Add '-1x' to each side of the equation. x + -1x = -11 + -1x Combine like terms: x + -1x = 0 0 = -11 + -1x Simplifying 0 = -11 + -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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