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Simplifying 2log(x + -1) + -1log(2x2 + 3x + -5) = 0 Reorder the terms: 2glo(-1 + x) + -1log(2x2 + 3x + -5) = 0 (-1 * 2glo + x * 2glo) + -1log(2x2 + 3x + -5) = 0 (-2glo + 2glox) + -1log(2x2 + 3x + -5) = 0 Reorder the terms: -2glo + 2glox + -1glo(-5 + 3x + 2x2) = 0 -2glo + 2glox + (-5 * -1glo + 3x * -1glo + 2x2 * -1glo) = 0 -2glo + 2glox + (5glo + -3glox + -2glox2) = 0 Reorder the terms: -2glo + 5glo + 2glox + -3glox + -2glox2 = 0 Combine like terms: -2glo + 5glo = 3glo 3glo + 2glox + -3glox + -2glox2 = 0 Combine like terms: 2glox + -3glox = -1glox 3glo + -1glox + -2glox2 = 0 Solving 3glo + -1glox + -2glox2 = 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), 'glo'. glo(3 + -1x + -2x2) = 0 Factor a trinomial. glo((1 + -1x)(3 + 2x)) = 0Subproblem 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 + -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.Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -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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