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Simplifying 2log(x + 1) = log(3x + 7) Reorder the terms: 2glo(1 + x) = log(3x + 7) (1 * 2glo + x * 2glo) = log(3x + 7) (2glo + 2glox) = log(3x + 7) Reorder the terms: 2glo + 2glox = glo(7 + 3x) 2glo + 2glox = (7 * glo + 3x * glo) 2glo + 2glox = (7glo + 3glox) Solving 2glo + 2glox = 7glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glo' to each side of the equation. 2glo + -7glo + 2glox = 7glo + -7glo + 3glox Combine like terms: 2glo + -7glo = -5glo -5glo + 2glox = 7glo + -7glo + 3glox Combine like terms: 7glo + -7glo = 0 -5glo + 2glox = 0 + 3glox -5glo + 2glox = 3glox Add '-3glox' to each side of the equation. -5glo + 2glox + -3glox = 3glox + -3glox Combine like terms: 2glox + -3glox = -1glox -5glo + -1glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -5glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(5 + x) = 0 Ignore the factor -1.Subproblem 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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