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Simplifying ln(x + 1) + ln(x + -5) = ln(3x + 2) Reorder the terms: ln(1 + x) + ln(x + -5) = ln(3x + 2) (1 * ln + x * ln) + ln(x + -5) = ln(3x + 2) (1ln + lnx) + ln(x + -5) = ln(3x + 2) Reorder the terms: 1ln + lnx + ln(-5 + x) = ln(3x + 2) 1ln + lnx + (-5 * ln + x * ln) = ln(3x + 2) 1ln + lnx + (-5ln + lnx) = ln(3x + 2) Reorder the terms: 1ln + -5ln + lnx + lnx = ln(3x + 2) Combine like terms: 1ln + -5ln = -4ln -4ln + lnx + lnx = ln(3x + 2) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(3x + 2) Reorder the terms: -4ln + 2lnx = ln(2 + 3x) -4ln + 2lnx = (2 * ln + 3x * ln) -4ln + 2lnx = (2ln + 3lnx) Solving -4ln + 2lnx = 2ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -4ln + -2ln + 2lnx = 2ln + -2ln + 3lnx Combine like terms: -4ln + -2ln = -6ln -6ln + 2lnx = 2ln + -2ln + 3lnx Combine like terms: 2ln + -2ln = 0 -6ln + 2lnx = 0 + 3lnx -6ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. -6ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx -6ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -6ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(6 + x) = 0 Ignore the factor -1.Subproblem 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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