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Simplifying log(3)(x2 + 2x) = log(3)(8) Reorder the terms: glo * 3(2x + x2) = log(3)(8) Reorder the terms for easier multiplication: 3glo(2x + x2) = log(3)(8) (2x * 3glo + x2 * 3glo) = log(3)(8) (6glox + 3glox2) = log(3)(8) Reorder the terms for easier multiplication: 6glox + 3glox2 = 3 * 8glo Multiply 3 * 8 6glox + 3glox2 = 24glo Solving 6glox + 3glox2 = 24glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-24glo' to each side of the equation. 6glox + -24glo + 3glox2 = 24glo + -24glo Reorder the terms: -24glo + 6glox + 3glox2 = 24glo + -24glo Combine like terms: 24glo + -24glo = 0 -24glo + 6glox + 3glox2 = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-8 + 2x + x2) = 0 Factor a trinomial. 3glo((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 3.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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Add 'x' to each side of the equation. -1x + x = 4 + x Combine like terms: -1x + x = 0 0 = 4 + x Simplifying 0 = 4 + 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 + -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. The solution to this equation could not be determined.
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