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Simplifying log(x2 + 2) = log(-8x + -13) Reorder the terms: glo(2 + x2) = log(-8x + -13) (2 * glo + x2 * glo) = log(-8x + -13) (2glo + glox2) = log(-8x + -13) Reorder the terms: 2glo + glox2 = glo(-13 + -8x) 2glo + glox2 = (-13 * glo + -8x * glo) 2glo + glox2 = (-13glo + -8glox) Solving 2glo + glox2 = -13glo + -8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '13glo' to each side of the equation. 2glo + 13glo + glox2 = -13glo + 13glo + -8glox Combine like terms: 2glo + 13glo = 15glo 15glo + glox2 = -13glo + 13glo + -8glox Combine like terms: -13glo + 13glo = 0 15glo + glox2 = 0 + -8glox 15glo + glox2 = -8glox Add '8glox' to each side of the equation. 15glo + 8glox + glox2 = -8glox + 8glox Combine like terms: -8glox + 8glox = 0 15glo + 8glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(15 + 8x + x2) = 0 Factor a trinomial. glo((5 + x)(3 + 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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