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