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Simplifying ln(x + 4) + ln(x + -1) = ln(6) Reorder the terms: ln(4 + x) + ln(x + -1) = ln(6) (4 * ln + x * ln) + ln(x + -1) = ln(6) (4ln + lnx) + ln(x + -1) = ln(6) Reorder the terms: 4ln + lnx + ln(-1 + x) = ln(6) 4ln + lnx + (-1 * ln + x * ln) = ln(6) 4ln + lnx + (-1ln + lnx) = ln(6) Reorder the terms: 4ln + -1ln + lnx + lnx = ln(6) Combine like terms: 4ln + -1ln = 3ln 3ln + lnx + lnx = ln(6) Combine like terms: lnx + lnx = 2lnx 3ln + 2lnx = ln(6) Reorder the terms for easier multiplication: 3ln + 2lnx = 6ln Solving 3ln + 2lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. 3ln + -6ln + 2lnx = 6ln + -6ln Combine like terms: 3ln + -6ln = -3ln -3ln + 2lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -3ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -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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