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Simplifying log[5](x2 + -6x) = log[5](x + 18) Reorder the terms: glo * 5(-6x + x2) = log[5](x + 18) Reorder the terms for easier multiplication: 5glo(-6x + x2) = log[5](x + 18) (-6x * 5glo + x2 * 5glo) = log[5](x + 18) (-30glox + 5glox2) = log[5](x + 18) Reorder the terms: -30glox + 5glox2 = glo * 5(18 + x) Reorder the terms for easier multiplication: -30glox + 5glox2 = 5glo(18 + x) -30glox + 5glox2 = (18 * 5glo + x * 5glo) -30glox + 5glox2 = (90glo + 5glox) Solving -30glox + 5glox2 = 90glo + 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-90glo' to each side of the equation. -30glox + -90glo + 5glox2 = 90glo + -90glo + 5glox Reorder the terms: -90glo + -30glox + 5glox2 = 90glo + -90glo + 5glox Combine like terms: 90glo + -90glo = 0 -90glo + -30glox + 5glox2 = 0 + 5glox -90glo + -30glox + 5glox2 = 5glox Add '-5glox' to each side of the equation. -90glo + -30glox + -5glox + 5glox2 = 5glox + -5glox Combine like terms: -30glox + -5glox = -35glox -90glo + -35glox + 5glox2 = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 -90glo + -35glox + 5glox2 = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-18 + -7x + x2) = 0 Factor a trinomial. 5glo((-2 + -1x)(9 + -1x)) = 0 Ignore the factor 5.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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Add 'x' to each side of the equation. -1x + x = -9 + x Combine like terms: -1x + x = 0 0 = -9 + x Simplifying 0 = -9 + 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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