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Simplifying log(x + -1) + log(x + -3) = log(3x + -7) Reorder the terms: glo(-1 + x) + log(x + -3) = log(3x + -7) (-1 * glo + x * glo) + log(x + -3) = log(3x + -7) (-1glo + glox) + log(x + -3) = log(3x + -7) Reorder the terms: -1glo + glox + glo(-3 + x) = log(3x + -7) -1glo + glox + (-3 * glo + x * glo) = log(3x + -7) -1glo + glox + (-3glo + glox) = log(3x + -7) Reorder the terms: -1glo + -3glo + glox + glox = log(3x + -7) Combine like terms: -1glo + -3glo = -4glo -4glo + glox + glox = log(3x + -7) Combine like terms: glox + glox = 2glox -4glo + 2glox = log(3x + -7) Reorder the terms: -4glo + 2glox = glo(-7 + 3x) -4glo + 2glox = (-7 * glo + 3x * glo) -4glo + 2glox = (-7glo + 3glox) Solving -4glo + 2glox = -7glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '7glo' to each side of the equation. -4glo + 7glo + 2glox = -7glo + 7glo + 3glox Combine like terms: -4glo + 7glo = 3glo 3glo + 2glox = -7glo + 7glo + 3glox Combine like terms: -7glo + 7glo = 0 3glo + 2glox = 0 + 3glox 3glo + 2glox = 3glox Add '-3glox' to each side of the equation. 3glo + 2glox + -3glox = 3glox + -3glox Combine like terms: 2glox + -3glox = -1glox 3glo + -1glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 3glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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