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Simplifying 2log(x + 2) = log(3x + 10) Reorder the terms: 2glo(2 + x) = log(3x + 10) (2 * 2glo + x * 2glo) = log(3x + 10) (4glo + 2glox) = log(3x + 10) Reorder the terms: 4glo + 2glox = glo(10 + 3x) 4glo + 2glox = (10 * glo + 3x * glo) 4glo + 2glox = (10glo + 3glox) Solving 4glo + 2glox = 10glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. 4glo + -10glo + 2glox = 10glo + -10glo + 3glox Combine like terms: 4glo + -10glo = -6glo -6glo + 2glox = 10glo + -10glo + 3glox Combine like terms: 10glo + -10glo = 0 -6glo + 2glox = 0 + 3glox -6glo + 2glox = 3glox Add '-3glox' to each side of the equation. -6glo + 2glox + -3glox = 3glox + -3glox Combine like terms: 2glox + -3glox = -1glox -6glo + -1glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -6glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(6 + 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -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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