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Simplifying log[8](3x + -1) = log[8](2x2) Reorder the terms: glo * 8(-1 + 3x) = log[8](2x2) Reorder the terms for easier multiplication: 8glo(-1 + 3x) = log[8](2x2) (-1 * 8glo + 3x * 8glo) = log[8](2x2) (-8glo + 24glox) = log[8](2x2) Remove parenthesis around (2x2) -8glo + 24glox = glo * 8 * 2x2 Reorder the terms for easier multiplication: -8glo + 24glox = 8 * 2glo * x2 Multiply 8 * 2 -8glo + 24glox = 16glo * x2 Multiply glo * x2 -8glo + 24glox = 16glox2 Solving -8glo + 24glox = 16glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-16glox2' to each side of the equation. -8glo + 24glox + -16glox2 = 16glox2 + -16glox2 Combine like terms: 16glox2 + -16glox2 = 0 -8glo + 24glox + -16glox2 = 0 Factor out the Greatest Common Factor (GCF), '8glo'. 8glo(-1 + 3x + -2x2) = 0 Factor a trinomial. 8glo((-1 + x)(1 + -2x)) = 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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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 '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Add '2x' to each side of the equation. -2x + 2x = -1 + 2x Combine like terms: -2x + 2x = 0 0 = -1 + 2x Simplifying 0 = -1 + 2x 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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