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Simplifying ln(x + -3) + ln(x + -2) = ln(6) Reorder the terms: ln(-3 + x) + ln(x + -2) = ln(6) (-3 * ln + x * ln) + ln(x + -2) = ln(6) (-3ln + lnx) + ln(x + -2) = ln(6) Reorder the terms: -3ln + lnx + ln(-2 + x) = ln(6) -3ln + lnx + (-2 * ln + x * ln) = ln(6) -3ln + lnx + (-2ln + lnx) = ln(6) Reorder the terms: -3ln + -2ln + lnx + lnx = ln(6) Combine like terms: -3ln + -2ln = -5ln -5ln + lnx + lnx = ln(6) Combine like terms: lnx + lnx = 2lnx -5ln + 2lnx = ln(6) Reorder the terms for easier multiplication: -5ln + 2lnx = 6ln Solving -5ln + 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. -5ln + -6ln + 2lnx = 6ln + -6ln Combine like terms: -5ln + -6ln = -11ln -11ln + 2lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -11ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-11 + 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 '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 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 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Add '-2x' to each side of the equation. 2x + -2x = 11 + -2x Combine like terms: 2x + -2x = 0 0 = 11 + -2x Simplifying 0 = 11 + -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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