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Simplifying log(3r + 7) = log(9 + -4r) Reorder the terms: glo(7 + 3r) = log(9 + -4r) (7 * glo + 3r * glo) = log(9 + -4r) (7glo + 3glor) = log(9 + -4r) 7glo + 3glor = (9 * glo + -4r * glo) 7glo + 3glor = (9glo + -4glor) Solving 7glo + 3glor = 9glo + -4glor Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glo' to each side of the equation. 7glo + -9glo + 3glor = 9glo + -9glo + -4glor Combine like terms: 7glo + -9glo = -2glo -2glo + 3glor = 9glo + -9glo + -4glor Combine like terms: 9glo + -9glo = 0 -2glo + 3glor = 0 + -4glor -2glo + 3glor = -4glor Add '4glor' to each side of the equation. -2glo + 3glor + 4glor = -4glor + 4glor Combine like terms: 3glor + 4glor = 7glor -2glo + 7glor = -4glor + 4glor Combine like terms: -4glor + 4glor = 0 -2glo + 7glor = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-2 + 7r) = 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 '(-2 + 7r)' equal to zero and attempt to solve: Simplifying -2 + 7r = 0 Solving -2 + 7r = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7r = 0 + 2 7r = 0 + 2 Combine like terms: 0 + 2 = 2 7r = 2 Add '-7r' to each side of the equation. 7r + -7r = 2 + -7r Combine like terms: 7r + -7r = 0 0 = 2 + -7r Simplifying 0 = 2 + -7r 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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