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