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Simplifying ln(x + -3) + ln(x + 1) = ln(6x + -18) Reorder the terms: ln(-3 + x) + ln(x + 1) = ln(6x + -18) (-3 * ln + x * ln) + ln(x + 1) = ln(6x + -18) (-3ln + lnx) + ln(x + 1) = ln(6x + -18) Reorder the terms: -3ln + lnx + ln(1 + x) = ln(6x + -18) -3ln + lnx + (1 * ln + x * ln) = ln(6x + -18) -3ln + lnx + (1ln + lnx) = ln(6x + -18) Reorder the terms: -3ln + 1ln + lnx + lnx = ln(6x + -18) Combine like terms: -3ln + 1ln = -2ln -2ln + lnx + lnx = ln(6x + -18) Combine like terms: lnx + lnx = 2lnx -2ln + 2lnx = ln(6x + -18) Reorder the terms: -2ln + 2lnx = ln(-18 + 6x) -2ln + 2lnx = (-18 * ln + 6x * ln) -2ln + 2lnx = (-18ln + 6lnx) Solving -2ln + 2lnx = -18ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '18ln' to each side of the equation. -2ln + 18ln + 2lnx = -18ln + 18ln + 6lnx Combine like terms: -2ln + 18ln = 16ln 16ln + 2lnx = -18ln + 18ln + 6lnx Combine like terms: -18ln + 18ln = 0 16ln + 2lnx = 0 + 6lnx 16ln + 2lnx = 6lnx Add '-6lnx' to each side of the equation. 16ln + 2lnx + -6lnx = 6lnx + -6lnx Combine like terms: 2lnx + -6lnx = -4lnx 16ln + -4lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 16ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(4 + -1x) = 0 Ignore the factor 4.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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