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Simplifying log(x2 + -3x + -13) = log(x + -1) Reorder the terms: glo(-13 + -3x + x2) = log(x + -1) (-13 * glo + -3x * glo + x2 * glo) = log(x + -1) (-13glo + -3glox + glox2) = log(x + -1) Reorder the terms: -13glo + -3glox + glox2 = glo(-1 + x) -13glo + -3glox + glox2 = (-1 * glo + x * glo) -13glo + -3glox + glox2 = (-1glo + glox) Solving -13glo + -3glox + glox2 = -1glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add 'glo' to each side of the equation. -13glo + -3glox + glo + glox2 = -1glo + glo + glox Reorder the terms: -13glo + glo + -3glox + glox2 = -1glo + glo + glox Combine like terms: -13glo + glo = -12glo -12glo + -3glox + glox2 = -1glo + glo + glox Combine like terms: -1glo + glo = 0 -12glo + -3glox + glox2 = 0 + glox -12glo + -3glox + glox2 = glox Add '-1glox' to each side of the equation. -12glo + -3glox + -1glox + glox2 = glox + -1glox Combine like terms: -3glox + -1glox = -4glox -12glo + -4glox + glox2 = glox + -1glox Combine like terms: glox + -1glox = 0 -12glo + -4glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-12 + -4x + x2) = 0 Factor a trinomial. glo((-2 + -1x)(6 + -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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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