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