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Simplifying log(x + 3) + log(x + -3) = log(x + 9) Reorder the terms: glo(3 + x) + log(x + -3) = log(x + 9) (3 * glo + x * glo) + log(x + -3) = log(x + 9) (3glo + glox) + log(x + -3) = log(x + 9) Reorder the terms: 3glo + glox + glo(-3 + x) = log(x + 9) 3glo + glox + (-3 * glo + x * glo) = log(x + 9) 3glo + glox + (-3glo + glox) = log(x + 9) Reorder the terms: 3glo + -3glo + glox + glox = log(x + 9) Combine like terms: 3glo + -3glo = 0 0 + glox + glox = log(x + 9) glox + glox = log(x + 9) Combine like terms: glox + glox = 2glox 2glox = log(x + 9) Reorder the terms: 2glox = glo(9 + x) 2glox = (9 * glo + x * glo) 2glox = (9glo + glox) Solving 2glox = 9glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glo' to each side of the equation. -9glo + 2glox = 9glo + -9glo + glox Combine like terms: 9glo + -9glo = 0 -9glo + 2glox = 0 + glox -9glo + 2glox = glox Add '-1glox' to each side of the equation. -9glo + 2glox + -1glox = glox + -1glox Combine like terms: 2glox + -1glox = 1glox -9glo + 1glox = glox + -1glox Combine like terms: glox + -1glox = 0 -9glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-9 + 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Add '-1x' to each side of the equation. x + -1x = 9 + -1x Combine like terms: x + -1x = 0 0 = 9 + -1x Simplifying 0 = 9 + -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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