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Simplifying ln(3 + -1x) + ln(x + 2) = ln(x + -4) (3 * ln + -1x * ln) + ln(x + 2) = ln(x + -4) (3ln + -1lnx) + ln(x + 2) = ln(x + -4) Reorder the terms: 3ln + -1lnx + ln(2 + x) = ln(x + -4) 3ln + -1lnx + (2 * ln + x * ln) = ln(x + -4) 3ln + -1lnx + (2ln + lnx) = ln(x + -4) Reorder the terms: 3ln + 2ln + -1lnx + lnx = ln(x + -4) Combine like terms: 3ln + 2ln = 5ln 5ln + -1lnx + lnx = ln(x + -4) Combine like terms: -1lnx + lnx = 0 5ln + 0 = ln(x + -4) 5ln = ln(x + -4) Reorder the terms: 5ln = ln(-4 + x) 5ln = (-4 * ln + x * ln) 5ln = (-4ln + lnx) Solving 5ln = -4ln + lnx 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. 5ln + 4ln = -4ln + 4ln + lnx Combine like terms: 5ln + 4ln = 9ln 9ln = -4ln + 4ln + lnx Combine like terms: -4ln + 4ln = 0 9ln = 0 + lnx 9ln = lnx Add '-1lnx' to each side of the equation. 9ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 9ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -1x) = 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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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