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