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Simplifying ln(x + 8) + -1ln(x + -2) = ln(x + 2) Reorder the terms: ln(8 + x) + -1ln(x + -2) = ln(x + 2) (8 * ln + x * ln) + -1ln(x + -2) = ln(x + 2) (8ln + lnx) + -1ln(x + -2) = ln(x + 2) Reorder the terms: 8ln + lnx + -1ln(-2 + x) = ln(x + 2) 8ln + lnx + (-2 * -1ln + x * -1ln) = ln(x + 2) 8ln + lnx + (2ln + -1lnx) = ln(x + 2) Reorder the terms: 8ln + 2ln + lnx + -1lnx = ln(x + 2) Combine like terms: 8ln + 2ln = 10ln 10ln + lnx + -1lnx = ln(x + 2) Combine like terms: lnx + -1lnx = 0 10ln + 0 = ln(x + 2) 10ln = ln(x + 2) Reorder the terms: 10ln = ln(2 + x) 10ln = (2 * ln + x * ln) 10ln = (2ln + lnx) Solving 10ln = 2ln + lnx 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. 10ln + -2ln = 2ln + -2ln + lnx Combine like terms: 10ln + -2ln = 8ln 8ln = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 8ln = 0 + lnx 8ln = lnx Add '-1lnx' to each side of the equation. 8ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 8ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(8 + -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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Add 'x' to each side of the equation. -1x + x = -8 + x Combine like terms: -1x + x = 0 0 = -8 + x Simplifying 0 = -8 + 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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