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Simplifying log(3x + -1) = log(5 + -2x) Reorder the terms: glo(-1 + 3x) = log(5 + -2x) (-1 * glo + 3x * glo) = log(5 + -2x) (-1glo + 3glox) = log(5 + -2x) -1glo + 3glox = (5 * glo + -2x * glo) -1glo + 3glox = (5glo + -2glox) Solving -1glo + 3glox = 5glo + -2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. -1glo + -5glo + 3glox = 5glo + -5glo + -2glox Combine like terms: -1glo + -5glo = -6glo -6glo + 3glox = 5glo + -5glo + -2glox Combine like terms: 5glo + -5glo = 0 -6glo + 3glox = 0 + -2glox -6glo + 3glox = -2glox Add '2glox' to each side of the equation. -6glo + 3glox + 2glox = -2glox + 2glox Combine like terms: 3glox + 2glox = 5glox -6glo + 5glox = -2glox + 2glox Combine like terms: -2glox + 2glox = 0 -6glo + 5glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-6 + 5x) = 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 '(-6 + 5x)' equal to zero and attempt to solve: Simplifying -6 + 5x = 0 Solving -6 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + 5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5x = 0 + 6 5x = 0 + 6 Combine like terms: 0 + 6 = 6 5x = 6 Add '-5x' to each side of the equation. 5x + -5x = 6 + -5x Combine like terms: 5x + -5x = 0 0 = 6 + -5x Simplifying 0 = 6 + -5x 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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