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Simplifying log(12x + -11) = log(3x + 13) Reorder the terms: glo(-11 + 12x) = log(3x + 13) (-11 * glo + 12x * glo) = log(3x + 13) (-11glo + 12glox) = log(3x + 13) Reorder the terms: -11glo + 12glox = glo(13 + 3x) -11glo + 12glox = (13 * glo + 3x * glo) -11glo + 12glox = (13glo + 3glox) Solving -11glo + 12glox = 13glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-13glo' to each side of the equation. -11glo + -13glo + 12glox = 13glo + -13glo + 3glox Combine like terms: -11glo + -13glo = -24glo -24glo + 12glox = 13glo + -13glo + 3glox Combine like terms: 13glo + -13glo = 0 -24glo + 12glox = 0 + 3glox -24glo + 12glox = 3glox Add '-3glox' to each side of the equation. -24glo + 12glox + -3glox = 3glox + -3glox Combine like terms: 12glox + -3glox = 9glox -24glo + 9glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -24glo + 9glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-8 + 3x) = 0 Ignore the factor 3.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 '(-8 + 3x)' equal to zero and attempt to solve: Simplifying -8 + 3x = 0 Solving -8 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x = 0 + 8 3x = 0 + 8 Combine like terms: 0 + 8 = 8 3x = 8 Add '-3x' to each side of the equation. 3x + -3x = 8 + -3x Combine like terms: 3x + -3x = 0 0 = 8 + -3x Simplifying 0 = 8 + -3x 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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