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Simplifying log(8)(x2 + 4x) = log(8)(12) Reorder the terms: glo * 8(4x + x2) = log(8)(12) Reorder the terms for easier multiplication: 8glo(4x + x2) = log(8)(12) (4x * 8glo + x2 * 8glo) = log(8)(12) (32glox + 8glox2) = log(8)(12) Reorder the terms for easier multiplication: 32glox + 8glox2 = 8 * 12glo Multiply 8 * 12 32glox + 8glox2 = 96glo Solving 32glox + 8glox2 = 96glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-96glo' to each side of the equation. 32glox + -96glo + 8glox2 = 96glo + -96glo Reorder the terms: -96glo + 32glox + 8glox2 = 96glo + -96glo Combine like terms: 96glo + -96glo = 0 -96glo + 32glox + 8glox2 = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(-12 + 4x + x2) = 0 Factor a trinomial. 8glo((-6 + -1x)(2 + -1x)) = 0 Ignore the factor 8.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 '(-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.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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