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Simplifying log(2x + -4) = log(3x + 5) Reorder the terms: glo(-4 + 2x) = log(3x + 5) (-4 * glo + 2x * glo) = log(3x + 5) (-4glo + 2glox) = log(3x + 5) Reorder the terms: -4glo + 2glox = glo(5 + 3x) -4glo + 2glox = (5 * glo + 3x * glo) -4glo + 2glox = (5glo + 3glox) Solving -4glo + 2glox = 5glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. -4glo + -5glo + 2glox = 5glo + -5glo + 3glox Combine like terms: -4glo + -5glo = -9glo -9glo + 2glox = 5glo + -5glo + 3glox Combine like terms: 5glo + -5glo = 0 -9glo + 2glox = 0 + 3glox -9glo + 2glox = 3glox Add '-3glox' to each side of the equation. -9glo + 2glox + -3glox = 3glox + -3glox Combine like terms: 2glox + -3glox = -1glox -9glo + -1glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -9glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(9 + 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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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