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