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Simplifying log[2](x2 + -6) = log[2](3x + 4) Reorder the terms: glo * 2(-6 + x2) = log[2](3x + 4) Reorder the terms for easier multiplication: 2glo(-6 + x2) = log[2](3x + 4) (-6 * 2glo + x2 * 2glo) = log[2](3x + 4) (-12glo + 2glox2) = log[2](3x + 4) Reorder the terms: -12glo + 2glox2 = glo * 2(4 + 3x) Reorder the terms for easier multiplication: -12glo + 2glox2 = 2glo(4 + 3x) -12glo + 2glox2 = (4 * 2glo + 3x * 2glo) -12glo + 2glox2 = (8glo + 6glox) Solving -12glo + 2glox2 = 8glo + 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. -12glo + -8glo + 2glox2 = 8glo + -8glo + 6glox Combine like terms: -12glo + -8glo = -20glo -20glo + 2glox2 = 8glo + -8glo + 6glox Combine like terms: 8glo + -8glo = 0 -20glo + 2glox2 = 0 + 6glox -20glo + 2glox2 = 6glox Add '-6glox' to each side of the equation. -20glo + -6glox + 2glox2 = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -20glo + -6glox + 2glox2 = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-10 + -3x + x2) = 0 Factor a trinomial. 2glo((-2 + -1x)(5 + -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 '(-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.Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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