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