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Simplifying log(2)(9x + 8) = log(2)(-1x2 + 2x + 16) Reorder the terms: glo * 2(8 + 9x) = log(2)(-1x2 + 2x + 16) Reorder the terms for easier multiplication: 2glo(8 + 9x) = log(2)(-1x2 + 2x + 16) (8 * 2glo + 9x * 2glo) = log(2)(-1x2 + 2x + 16) (16glo + 18glox) = log(2)(-1x2 + 2x + 16) Reorder the terms: 16glo + 18glox = glo * 2(16 + 2x + -1x2) Reorder the terms for easier multiplication: 16glo + 18glox = 2glo(16 + 2x + -1x2) 16glo + 18glox = (16 * 2glo + 2x * 2glo + -1x2 * 2glo) 16glo + 18glox = (32glo + 4glox + -2glox2) Solving 16glo + 18glox = 32glo + 4glox + -2glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-32glo' to each side of the equation. 16glo + -32glo + 18glox = 32glo + 4glox + -32glo + -2glox2 Combine like terms: 16glo + -32glo = -16glo -16glo + 18glox = 32glo + 4glox + -32glo + -2glox2 Reorder the terms: -16glo + 18glox = 32glo + -32glo + 4glox + -2glox2 Combine like terms: 32glo + -32glo = 0 -16glo + 18glox = 0 + 4glox + -2glox2 -16glo + 18glox = 4glox + -2glox2 Add '-4glox' to each side of the equation. -16glo + 18glox + -4glox = 4glox + -4glox + -2glox2 Combine like terms: 18glox + -4glox = 14glox -16glo + 14glox = 4glox + -4glox + -2glox2 Combine like terms: 4glox + -4glox = 0 -16glo + 14glox = 0 + -2glox2 -16glo + 14glox = -2glox2 Add '2glox2' to each side of the equation. -16glo + 14glox + 2glox2 = -2glox2 + 2glox2 Combine like terms: -2glox2 + 2glox2 = 0 -16glo + 14glox + 2glox2 = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-8 + 7x + x2) = 0 Factor a trinomial. 2glo((-8 + -1x)(1 + -1x)) = 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 '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Add 'x' to each side of the equation. -1x + x = 8 + x Combine like terms: -1x + x = 0 0 = 8 + x Simplifying 0 = 8 + 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 '(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. The solution to this equation could not be determined.
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