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Simplifying log(16 + 2b) = log(b2 + -4b) (16 * glo + 2b * glo) = log(b2 + -4b) Reorder the terms: (2bglo + 16glo) = log(b2 + -4b) (2bglo + 16glo) = log(b2 + -4b) Reorder the terms: 2bglo + 16glo = glo(-4b + b2) 2bglo + 16glo = (-4b * glo + b2 * glo) 2bglo + 16glo = (-4bglo + b2glo) Solving 2bglo + 16glo = -4bglo + b2glo Solving for variable 'b'. Reorder the terms: 2bglo + 4bglo + -1b2glo + 16glo = -4bglo + b2glo + 4bglo + -1b2glo Combine like terms: 2bglo + 4bglo = 6bglo 6bglo + -1b2glo + 16glo = -4bglo + b2glo + 4bglo + -1b2glo Reorder the terms: 6bglo + -1b2glo + 16glo = -4bglo + 4bglo + b2glo + -1b2glo Combine like terms: -4bglo + 4bglo = 0 6bglo + -1b2glo + 16glo = 0 + b2glo + -1b2glo 6bglo + -1b2glo + 16glo = b2glo + -1b2glo Combine like terms: b2glo + -1b2glo = 0 6bglo + -1b2glo + 16glo = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(6b + -1b2 + 16) = 0 Factor a trinomial. glo((-1b + -2)(b + -8)) = 0Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing b to the left, all other terms to the right. Add '-1glo' to each side of the equation. glo + -1glo = 0 + -1glo Remove the zero: 0 = -1glo Simplifying 0 = -1glo 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 '(-1b + -2)' equal to zero and attempt to solve: Simplifying -1b + -2 = 0 Reorder the terms: -2 + -1b = 0 Solving -2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1b = 0 + 2 -1b = 0 + 2 Combine like terms: 0 + 2 = 2 -1b = 2 Divide each side by '-1'. b = -2 Simplifying b = -2Subproblem 3
Set the factor '(b + -8)' equal to zero and attempt to solve: Simplifying b + -8 = 0 Reorder the terms: -8 + b = 0 Solving -8 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + b = 0 + 8 b = 0 + 8 Combine like terms: 0 + 8 = 8 b = 8 Simplifying b = 8Solution
b = {-2, 8}
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