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