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Simplifying log(3)(5x + -5) + -1log(3)(x2 + -1) = 0 Reorder the terms: glo * 3(-5 + 5x) + -1log(3)(x2 + -1) = 0 Reorder the terms for easier multiplication: 3glo(-5 + 5x) + -1log(3)(x2 + -1) = 0 (-5 * 3glo + 5x * 3glo) + -1log(3)(x2 + -1) = 0 (-15glo + 15glox) + -1log(3)(x2 + -1) = 0 Reorder the terms: -15glo + 15glox + -1glo * 3(-1 + x2) = 0 Reorder the terms for easier multiplication: -15glo + 15glox + -1 * 3glo(-1 + x2) = 0 Multiply -1 * 3 -15glo + 15glox + -3glo(-1 + x2) = 0 -15glo + 15glox + (-1 * -3glo + x2 * -3glo) = 0 -15glo + 15glox + (3glo + -3glox2) = 0 Reorder the terms: -15glo + 3glo + 15glox + -3glox2 = 0 Combine like terms: -15glo + 3glo = -12glo -12glo + 15glox + -3glox2 = 0 Solving -12glo + 15glox + -3glox2 = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-4 + 5x + -1x2) = 0 Factor a trinomial. 3glo((-4 + x)(1 + -1x)) = 0 Ignore the factor 3.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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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