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Simplifying log(x2) + -1log(x) = 2log(x + -1) Multiply glo * x2 glox2 + -1log(x) = 2log(x + -1) Multiply glo * x glox2 + -1glox = 2log(x + -1) Reorder the terms: -1glox + glox2 = 2log(x + -1) Reorder the terms: -1glox + glox2 = 2glo(-1 + x) -1glox + glox2 = (-1 * 2glo + x * 2glo) -1glox + glox2 = (-2glo + 2glox) Solving -1glox + glox2 = -2glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. -1glox + 2glo + glox2 = -2glo + 2glo + 2glox Reorder the terms: 2glo + -1glox + glox2 = -2glo + 2glo + 2glox Combine like terms: -2glo + 2glo = 0 2glo + -1glox + glox2 = 0 + 2glox 2glo + -1glox + glox2 = 2glox Add '-2glox' to each side of the equation. 2glo + -1glox + -2glox + glox2 = 2glox + -2glox Combine like terms: -1glox + -2glox = -3glox 2glo + -3glox + glox2 = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 2glo + -3glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(2 + -3x + x2) = 0 Factor a trinomial. glo((1 + -1x)(2 + -1x)) = 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 '(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. The solution to this equation could not be determined.
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