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