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Simplifying ln(x + -3) + ln(x + 4) = 3ln(2) Reorder the terms: ln(-3 + x) + ln(x + 4) = 3ln(2) (-3 * ln + x * ln) + ln(x + 4) = 3ln(2) (-3ln + lnx) + ln(x + 4) = 3ln(2) Reorder the terms: -3ln + lnx + ln(4 + x) = 3ln(2) -3ln + lnx + (4 * ln + x * ln) = 3ln(2) -3ln + lnx + (4ln + lnx) = 3ln(2) Reorder the terms: -3ln + 4ln + lnx + lnx = 3ln(2) Combine like terms: -3ln + 4ln = 1ln 1ln + lnx + lnx = 3ln(2) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = 3ln(2) Reorder the terms for easier multiplication: 1ln + 2lnx = 3 * 2ln Multiply 3 * 2 1ln + 2lnx = 6ln Solving 1ln + 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. 1ln + -6ln + 2lnx = 6ln + -6ln Combine like terms: 1ln + -6ln = -5ln -5ln + 2lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 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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