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Simplifying log(3x + 7) = log(2x + 8) Reorder the terms: glo(7 + 3x) = log(2x + 8) (7 * glo + 3x * glo) = log(2x + 8) (7glo + 3glox) = log(2x + 8) Reorder the terms: 7glo + 3glox = glo(8 + 2x) 7glo + 3glox = (8 * glo + 2x * glo) 7glo + 3glox = (8glo + 2glox) Solving 7glo + 3glox = 8glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. 7glo + -8glo + 3glox = 8glo + -8glo + 2glox Combine like terms: 7glo + -8glo = -1glo -1glo + 3glox = 8glo + -8glo + 2glox Combine like terms: 8glo + -8glo = 0 -1glo + 3glox = 0 + 2glox -1glo + 3glox = 2glox Add '-2glox' to each side of the equation. -1glo + 3glox + -2glox = 2glox + -2glox Combine like terms: 3glox + -2glox = 1glox -1glo + 1glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 -1glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-1 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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