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Simplifying log(6)(5 + -3x) = log(6)(x2 + -5) Reorder the terms for easier multiplication: 6glo(5 + -3x) = log(6)(x2 + -5) (5 * 6glo + -3x * 6glo) = log(6)(x2 + -5) (30glo + -18glox) = log(6)(x2 + -5) Reorder the terms: 30glo + -18glox = glo * 6(-5 + x2) Reorder the terms for easier multiplication: 30glo + -18glox = 6glo(-5 + x2) 30glo + -18glox = (-5 * 6glo + x2 * 6glo) 30glo + -18glox = (-30glo + 6glox2) Solving 30glo + -18glox = -30glo + 6glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '30glo' to each side of the equation. 30glo + 30glo + -18glox = -30glo + 30glo + 6glox2 Combine like terms: 30glo + 30glo = 60glo 60glo + -18glox = -30glo + 30glo + 6glox2 Combine like terms: -30glo + 30glo = 0 60glo + -18glox = 0 + 6glox2 60glo + -18glox = 6glox2 Add '-6glox2' to each side of the equation. 60glo + -18glox + -6glox2 = 6glox2 + -6glox2 Combine like terms: 6glox2 + -6glox2 = 0 60glo + -18glox + -6glox2 = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(10 + -3x + -1x2) = 0 Factor a trinomial. 6glo((2 + -1x)(5 + x)) = 0 Ignore the factor 6.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 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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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