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Simplifying log(x + 1) + log(x + -3) = log(6x2 + -6) Reorder the terms: glo(1 + x) + log(x + -3) = log(6x2 + -6) (1 * glo + x * glo) + log(x + -3) = log(6x2 + -6) (1glo + glox) + log(x + -3) = log(6x2 + -6) Reorder the terms: 1glo + glox + glo(-3 + x) = log(6x2 + -6) 1glo + glox + (-3 * glo + x * glo) = log(6x2 + -6) 1glo + glox + (-3glo + glox) = log(6x2 + -6) Reorder the terms: 1glo + -3glo + glox + glox = log(6x2 + -6) Combine like terms: 1glo + -3glo = -2glo -2glo + glox + glox = log(6x2 + -6) Combine like terms: glox + glox = 2glox -2glo + 2glox = log(6x2 + -6) Reorder the terms: -2glo + 2glox = glo(-6 + 6x2) -2glo + 2glox = (-6 * glo + 6x2 * glo) -2glo + 2glox = (-6glo + 6glox2) Solving -2glo + 2glox = -6glo + 6glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6glo' to each side of the equation. -2glo + 6glo + 2glox = -6glo + 6glo + 6glox2 Combine like terms: -2glo + 6glo = 4glo 4glo + 2glox = -6glo + 6glo + 6glox2 Combine like terms: -6glo + 6glo = 0 4glo + 2glox = 0 + 6glox2 4glo + 2glox = 6glox2 Add '-6glox2' to each side of the equation. 4glo + 2glox + -6glox2 = 6glox2 + -6glox2 Combine like terms: 6glox2 + -6glox2 = 0 4glo + 2glox + -6glox2 = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(2 + x + -3x2) = 0 Factor a trinomial. 2glo((1 + -1x)(2 + 3x)) = 0 Ignore the factor 2.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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Add '-3x' to each side of the equation. 3x + -3x = -2 + -3x Combine like terms: 3x + -3x = 0 0 = -2 + -3x Simplifying 0 = -2 + -3x 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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