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Simplifying ln(x + 4) = ln(x + 2) + -1ln(x + 4) Reorder the terms: ln(4 + x) = ln(x + 2) + -1ln(x + 4) (4 * ln + x * ln) = ln(x + 2) + -1ln(x + 4) (4ln + lnx) = ln(x + 2) + -1ln(x + 4) Reorder the terms: 4ln + lnx = ln(2 + x) + -1ln(x + 4) 4ln + lnx = (2 * ln + x * ln) + -1ln(x + 4) 4ln + lnx = (2ln + lnx) + -1ln(x + 4) Reorder the terms: 4ln + lnx = 2ln + lnx + -1ln(4 + x) 4ln + lnx = 2ln + lnx + (4 * -1ln + x * -1ln) 4ln + lnx = 2ln + lnx + (-4ln + -1lnx) Reorder the terms: 4ln + lnx = 2ln + -4ln + lnx + -1lnx Combine like terms: 2ln + -4ln = -2ln 4ln + lnx = -2ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 4ln + lnx = -2ln + 0 4ln + lnx = -2ln Solving 4ln + lnx = -2ln 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 + lnx = -2ln + 2ln Combine like terms: 4ln + 2ln = 6ln 6ln + lnx = -2ln + 2ln Combine like terms: -2ln + 2ln = 0 6ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + x) = 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 '(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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