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Simplifying log(5x + -2) = log(3x + 1) Reorder the terms: glo(-2 + 5x) = log(3x + 1) (-2 * glo + 5x * glo) = log(3x + 1) (-2glo + 5glox) = log(3x + 1) Reorder the terms: -2glo + 5glox = glo(1 + 3x) -2glo + 5glox = (1 * glo + 3x * glo) -2glo + 5glox = (1glo + 3glox) Solving -2glo + 5glox = 1glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-1glo' to each side of the equation. -2glo + -1glo + 5glox = 1glo + -1glo + 3glox Combine like terms: -2glo + -1glo = -3glo -3glo + 5glox = 1glo + -1glo + 3glox Combine like terms: 1glo + -1glo = 0 -3glo + 5glox = 0 + 3glox -3glo + 5glox = 3glox Add '-3glox' to each side of the equation. -3glo + 5glox + -3glox = 3glox + -3glox Combine like terms: 5glox + -3glox = 2glox -3glo + 2glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 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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