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Simplifying ln(x + 12) + -1ln(x + -2) = ln(x + 4) Reorder the terms: ln(12 + x) + -1ln(x + -2) = ln(x + 4) (12 * ln + x * ln) + -1ln(x + -2) = ln(x + 4) (12ln + lnx) + -1ln(x + -2) = ln(x + 4) Reorder the terms: 12ln + lnx + -1ln(-2 + x) = ln(x + 4) 12ln + lnx + (-2 * -1ln + x * -1ln) = ln(x + 4) 12ln + lnx + (2ln + -1lnx) = ln(x + 4) Reorder the terms: 12ln + 2ln + lnx + -1lnx = ln(x + 4) Combine like terms: 12ln + 2ln = 14ln 14ln + lnx + -1lnx = ln(x + 4) Combine like terms: lnx + -1lnx = 0 14ln + 0 = ln(x + 4) 14ln = ln(x + 4) Reorder the terms: 14ln = ln(4 + x) 14ln = (4 * ln + x * ln) 14ln = (4ln + lnx) Solving 14ln = 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. 14ln + -4ln = 4ln + -4ln + lnx Combine like terms: 14ln + -4ln = 10ln 10ln = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 10ln = 0 + lnx 10ln = lnx Add '-1lnx' to each side of the equation. 10ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 10ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + 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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