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Simplifying log(x + 2) + log(x + -1) = log(13 + -2x) Reorder the terms: glo(2 + x) + log(x + -1) = log(13 + -2x) (2 * glo + x * glo) + log(x + -1) = log(13 + -2x) (2glo + glox) + log(x + -1) = log(13 + -2x) Reorder the terms: 2glo + glox + glo(-1 + x) = log(13 + -2x) 2glo + glox + (-1 * glo + x * glo) = log(13 + -2x) 2glo + glox + (-1glo + glox) = log(13 + -2x) Reorder the terms: 2glo + -1glo + glox + glox = log(13 + -2x) Combine like terms: 2glo + -1glo = 1glo 1glo + glox + glox = log(13 + -2x) Combine like terms: glox + glox = 2glox 1glo + 2glox = log(13 + -2x) 1glo + 2glox = (13 * glo + -2x * glo) 1glo + 2glox = (13glo + -2glox) Solving 1glo + 2glox = 13glo + -2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-13glo' to each side of the equation. 1glo + -13glo + 2glox = 13glo + -13glo + -2glox Combine like terms: 1glo + -13glo = -12glo -12glo + 2glox = 13glo + -13glo + -2glox Combine like terms: 13glo + -13glo = 0 -12glo + 2glox = 0 + -2glox -12glo + 2glox = -2glox Add '2glox' to each side of the equation. -12glo + 2glox + 2glox = -2glox + 2glox Combine like terms: 2glox + 2glox = 4glox -12glo + 4glox = -2glox + 2glox Combine like terms: -2glox + 2glox = 0 -12glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '4glo'. 4glo(-3 + x) = 0 Ignore the factor 4.Subproblem 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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