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Simplifying log(x + 3) + log(x + -1) = log(1 + -1x) Reorder the terms: glo(3 + x) + log(x + -1) = log(1 + -1x) (3 * glo + x * glo) + log(x + -1) = log(1 + -1x) (3glo + glox) + log(x + -1) = log(1 + -1x) Reorder the terms: 3glo + glox + glo(-1 + x) = log(1 + -1x) 3glo + glox + (-1 * glo + x * glo) = log(1 + -1x) 3glo + glox + (-1glo + glox) = log(1 + -1x) Reorder the terms: 3glo + -1glo + glox + glox = log(1 + -1x) Combine like terms: 3glo + -1glo = 2glo 2glo + glox + glox = log(1 + -1x) Combine like terms: glox + glox = 2glox 2glo + 2glox = log(1 + -1x) 2glo + 2glox = (1 * glo + -1x * glo) 2glo + 2glox = (1glo + -1glox) Solving 2glo + 2glox = 1glo + -1glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. 2glo + -1glo + 2glox = 1glo + -1glo + -1glox Combine like terms: 2glo + -1glo = 1glo 1glo + 2glox = 1glo + -1glo + -1glox Combine like terms: 1glo + -1glo = 0 1glo + 2glox = 0 + -1glox 1glo + 2glox = -1glox Add 'glox' to each side of the equation. 1glo + 2glox + glox = -1glox + glox Combine like terms: 2glox + glox = 3glox 1glo + 3glox = -1glox + glox Combine like terms: -1glox + glox = 0 1glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(1 + 3x) = 0Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -3x 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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