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Simplifying 2ln(x + 1) + ln(x + -5) = ln(x3 + -4) Reorder the terms: 2ln(1 + x) + ln(x + -5) = ln(x3 + -4) (1 * 2ln + x * 2ln) + ln(x + -5) = ln(x3 + -4) (2ln + 2lnx) + ln(x + -5) = ln(x3 + -4) Reorder the terms: 2ln + 2lnx + ln(-5 + x) = ln(x3 + -4) 2ln + 2lnx + (-5 * ln + x * ln) = ln(x3 + -4) 2ln + 2lnx + (-5ln + lnx) = ln(x3 + -4) Reorder the terms: 2ln + -5ln + 2lnx + lnx = ln(x3 + -4) Combine like terms: 2ln + -5ln = -3ln -3ln + 2lnx + lnx = ln(x3 + -4) Combine like terms: 2lnx + lnx = 3lnx -3ln + 3lnx = ln(x3 + -4) Reorder the terms: -3ln + 3lnx = ln(-4 + x3) -3ln + 3lnx = (-4 * ln + x3 * ln) -3ln + 3lnx = (-4ln + lnx3) Solving -3ln + 3lnx = -4ln + lnx3 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '4ln' to each side of the equation. -3ln + 4ln + 3lnx = -4ln + 4ln + lnx3 Combine like terms: -3ln + 4ln = 1ln 1ln + 3lnx = -4ln + 4ln + lnx3 Combine like terms: -4ln + 4ln = 0 1ln + 3lnx = 0 + lnx3 1ln + 3lnx = lnx3 Add '-1lnx3' to each side of the equation. 1ln + 3lnx + -1lnx3 = lnx3 + -1lnx3 Combine like terms: lnx3 + -1lnx3 = 0 1ln + 3lnx + -1lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + 3x + -1x3) = 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 '(1 + 3x + -1x3)' equal to zero and attempt to solve: Simplifying 1 + 3x + -1x3 = 0 Solving 1 + 3x + -1x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 3x + -1 + -1x3 = 0 + -1 Reorder the terms: 1 + -1 + 3x + -1x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x + -1x3 = 0 + -1 3x + -1x3 = 0 + -1 Combine like terms: 0 + -1 = -1 3x + -1x3 = -1 Add '-3x' to each side of the equation. 3x + -3x + -1x3 = -1 + -3x Combine like terms: 3x + -3x = 0 0 + -1x3 = -1 + -3x -1x3 = -1 + -3x Add 'x3' to each side of the equation. -1x3 + x3 = -1 + -3x + x3 Combine like terms: -1x3 + x3 = 0 0 = -1 + -3x + x3 Simplifying 0 = -1 + -3x + x3 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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