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Simplifying log(x + 2) + log(x + 4) = log(x + 8) Reorder the terms: glo(2 + x) + log(x + 4) = log(x + 8) (2 * glo + x * glo) + log(x + 4) = log(x + 8) (2glo + glox) + log(x + 4) = log(x + 8) Reorder the terms: 2glo + glox + glo(4 + x) = log(x + 8) 2glo + glox + (4 * glo + x * glo) = log(x + 8) 2glo + glox + (4glo + glox) = log(x + 8) Reorder the terms: 2glo + 4glo + glox + glox = log(x + 8) Combine like terms: 2glo + 4glo = 6glo 6glo + glox + glox = log(x + 8) Combine like terms: glox + glox = 2glox 6glo + 2glox = log(x + 8) Reorder the terms: 6glo + 2glox = glo(8 + x) 6glo + 2glox = (8 * glo + x * glo) 6glo + 2glox = (8glo + glox) Solving 6glo + 2glox = 8glo + glox 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. 6glo + -8glo + 2glox = 8glo + -8glo + glox Combine like terms: 6glo + -8glo = -2glo -2glo + 2glox = 8glo + -8glo + glox Combine like terms: 8glo + -8glo = 0 -2glo + 2glox = 0 + glox -2glo + 2glox = glox Add '-1glox' to each side of the equation. -2glo + 2glox + -1glox = glox + -1glox Combine like terms: 2glox + -1glox = 1glox -2glo + 1glox = glox + -1glox Combine like terms: glox + -1glox = 0 -2glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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