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Simplifying log(5x + -3) = log(3x + 7) Reorder the terms: glo(-3 + 5x) = log(3x + 7) (-3 * glo + 5x * glo) = log(3x + 7) (-3glo + 5glox) = log(3x + 7) Reorder the terms: -3glo + 5glox = glo(7 + 3x) -3glo + 5glox = (7 * glo + 3x * glo) -3glo + 5glox = (7glo + 3glox) Solving -3glo + 5glox = 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. -3glo + -7glo + 5glox = 7glo + -7glo + 3glox Combine like terms: -3glo + -7glo = -10glo -10glo + 5glox = 7glo + -7glo + 3glox Combine like terms: 7glo + -7glo = 0 -10glo + 5glox = 0 + 3glox -10glo + 5glox = 3glox Add '-3glox' to each side of the equation. -10glo + 5glox + -3glox = 3glox + -3glox Combine like terms: 5glox + -3glox = 2glox -10glo + 2glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -10glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-5 + x) = 0 Ignore the factor 2.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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