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Simplifying log(3x + -2) + log(3x + -1) = log(4x + -3) * 2 Reorder the terms: glo(-2 + 3x) + log(3x + -1) = log(4x + -3) * 2 (-2 * glo + 3x * glo) + log(3x + -1) = log(4x + -3) * 2 (-2glo + 3glox) + log(3x + -1) = log(4x + -3) * 2 Reorder the terms: -2glo + 3glox + glo(-1 + 3x) = log(4x + -3) * 2 -2glo + 3glox + (-1 * glo + 3x * glo) = log(4x + -3) * 2 -2glo + 3glox + (-1glo + 3glox) = log(4x + -3) * 2 Reorder the terms: -2glo + -1glo + 3glox + 3glox = log(4x + -3) * 2 Combine like terms: -2glo + -1glo = -3glo -3glo + 3glox + 3glox = log(4x + -3) * 2 Combine like terms: 3glox + 3glox = 6glox -3glo + 6glox = log(4x + -3) * 2 Reorder the terms: -3glo + 6glox = glo(-3 + 4x) * 2 Reorder the terms for easier multiplication: -3glo + 6glox = 2glo(-3 + 4x) -3glo + 6glox = (-3 * 2glo + 4x * 2glo) -3glo + 6glox = (-6glo + 8glox) Solving -3glo + 6glox = -6glo + 8glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '6glo' to each side of the equation. -3glo + 6glo + 6glox = -6glo + 6glo + 8glox Combine like terms: -3glo + 6glo = 3glo 3glo + 6glox = -6glo + 6glo + 8glox Combine like terms: -6glo + 6glo = 0 3glo + 6glox = 0 + 8glox 3glo + 6glox = 8glox Add '-8glox' to each side of the equation. 3glo + 6glox + -8glox = 8glox + -8glox Combine like terms: 6glox + -8glox = -2glox 3glo + -2glox = 8glox + -8glox Combine like terms: 8glox + -8glox = 0 3glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(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 '(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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