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Simplifying ln(x + -2) = ln(3x + 6) Reorder the terms: ln(-2 + x) = ln(3x + 6) (-2 * ln + x * ln) = ln(3x + 6) (-2ln + lnx) = ln(3x + 6) Reorder the terms: -2ln + lnx = ln(6 + 3x) -2ln + lnx = (6 * ln + 3x * ln) -2ln + lnx = (6ln + 3lnx) Solving -2ln + lnx = 6ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -2ln + -6ln + lnx = 6ln + -6ln + 3lnx Combine like terms: -2ln + -6ln = -8ln -8ln + lnx = 6ln + -6ln + 3lnx Combine like terms: 6ln + -6ln = 0 -8ln + lnx = 0 + 3lnx -8ln + lnx = 3lnx Add '-3lnx' to each side of the equation. -8ln + lnx + -3lnx = 3lnx + -3lnx Combine like terms: lnx + -3lnx = -2lnx -8ln + -2lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -8ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-2ln'. -2ln(4 + x) = 0 Ignore the factor -2.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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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