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Simplifying log(x + -8) + log(x + -2) = log(8 + -1x) Reorder the terms: glo(-8 + x) + log(x + -2) = log(8 + -1x) (-8 * glo + x * glo) + log(x + -2) = log(8 + -1x) (-8glo + glox) + log(x + -2) = log(8 + -1x) Reorder the terms: -8glo + glox + glo(-2 + x) = log(8 + -1x) -8glo + glox + (-2 * glo + x * glo) = log(8 + -1x) -8glo + glox + (-2glo + glox) = log(8 + -1x) Reorder the terms: -8glo + -2glo + glox + glox = log(8 + -1x) Combine like terms: -8glo + -2glo = -10glo -10glo + glox + glox = log(8 + -1x) Combine like terms: glox + glox = 2glox -10glo + 2glox = log(8 + -1x) -10glo + 2glox = (8 * glo + -1x * glo) -10glo + 2glox = (8glo + -1glox) Solving -10glo + 2glox = 8glo + -1glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. -10glo + -8glo + 2glox = 8glo + -8glo + -1glox Combine like terms: -10glo + -8glo = -18glo -18glo + 2glox = 8glo + -8glo + -1glox Combine like terms: 8glo + -8glo = 0 -18glo + 2glox = 0 + -1glox -18glo + 2glox = -1glox Add 'glox' to each side of the equation. -18glo + 2glox + glox = -1glox + glox Combine like terms: 2glox + glox = 3glox -18glo + 3glox = -1glox + glox Combine like terms: -1glox + glox = 0 -18glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-6 + 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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Add '-1x' to each side of the equation. x + -1x = 6 + -1x Combine like terms: x + -1x = 0 0 = 6 + -1x Simplifying 0 = 6 + -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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