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Simplifying log(2x + 1) + log(x + -4) = log(2x2 + -4) Reorder the terms: glo(1 + 2x) + log(x + -4) = log(2x2 + -4) (1 * glo + 2x * glo) + log(x + -4) = log(2x2 + -4) (1glo + 2glox) + log(x + -4) = log(2x2 + -4) Reorder the terms: 1glo + 2glox + glo(-4 + x) = log(2x2 + -4) 1glo + 2glox + (-4 * glo + x * glo) = log(2x2 + -4) 1glo + 2glox + (-4glo + glox) = log(2x2 + -4) Reorder the terms: 1glo + -4glo + 2glox + glox = log(2x2 + -4) Combine like terms: 1glo + -4glo = -3glo -3glo + 2glox + glox = log(2x2 + -4) Combine like terms: 2glox + glox = 3glox -3glo + 3glox = log(2x2 + -4) Reorder the terms: -3glo + 3glox = glo(-4 + 2x2) -3glo + 3glox = (-4 * glo + 2x2 * glo) -3glo + 3glox = (-4glo + 2glox2) Solving -3glo + 3glox = -4glo + 2glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4glo' to each side of the equation. -3glo + 4glo + 3glox = -4glo + 4glo + 2glox2 Combine like terms: -3glo + 4glo = 1glo 1glo + 3glox = -4glo + 4glo + 2glox2 Combine like terms: -4glo + 4glo = 0 1glo + 3glox = 0 + 2glox2 1glo + 3glox = 2glox2 Add '-2glox2' to each side of the equation. 1glo + 3glox + -2glox2 = 2glox2 + -2glox2 Combine like terms: 2glox2 + -2glox2 = 0 1glo + 3glox + -2glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(1 + 3x + -2x2) = 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 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + -2x2 = 0 Solving 1 + 3x + -2x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 3x + -1 + -2x2 = 0 + -1 Reorder the terms: 1 + -1 + 3x + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x + -2x2 = 0 + -1 3x + -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3x + -2x2 = -1 Add '-3x' to each side of the equation. 3x + -3x + -2x2 = -1 + -3x Combine like terms: 3x + -3x = 0 0 + -2x2 = -1 + -3x -2x2 = -1 + -3x Add '2x2' to each side of the equation. -2x2 + 2x2 = -1 + -3x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 = -1 + -3x + 2x2 Simplifying 0 = -1 + -3x + 2x2 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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