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