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Simplifying ln(x + -6) + ln(x + 5) = ln(x + -31) Reorder the terms: ln(-6 + x) + ln(x + 5) = ln(x + -31) (-6 * ln + x * ln) + ln(x + 5) = ln(x + -31) (-6ln + lnx) + ln(x + 5) = ln(x + -31) Reorder the terms: -6ln + lnx + ln(5 + x) = ln(x + -31) -6ln + lnx + (5 * ln + x * ln) = ln(x + -31) -6ln + lnx + (5ln + lnx) = ln(x + -31) Reorder the terms: -6ln + 5ln + lnx + lnx = ln(x + -31) Combine like terms: -6ln + 5ln = -1ln -1ln + lnx + lnx = ln(x + -31) Combine like terms: lnx + lnx = 2lnx -1ln + 2lnx = ln(x + -31) Reorder the terms: -1ln + 2lnx = ln(-31 + x) -1ln + 2lnx = (-31 * ln + x * ln) -1ln + 2lnx = (-31ln + lnx) Solving -1ln + 2lnx = -31ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '31ln' to each side of the equation. -1ln + 31ln + 2lnx = -31ln + 31ln + lnx Combine like terms: -1ln + 31ln = 30ln 30ln + 2lnx = -31ln + 31ln + lnx Combine like terms: -31ln + 31ln = 0 30ln + 2lnx = 0 + lnx 30ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 30ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 30ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 30ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(30 + 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 '(30 + x)' equal to zero and attempt to solve: Simplifying 30 + x = 0 Solving 30 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + x = 0 + -30 x = 0 + -30 Combine like terms: 0 + -30 = -30 x = -30 Add '-1x' to each side of the equation. x + -1x = -30 + -1x Combine like terms: x + -1x = 0 0 = -30 + -1x Simplifying 0 = -30 + -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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