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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 = 2glo 2glo + 12glox = -13glo + 13glo + 3glox Combine like terms: -13glo + 13glo = 0 2glo + 12glox = 0 + 3glox 2glo + 12glox = 3glox Add '-3glox' to each side of the equation. 2glo + 12glox + -3glox = 3glox + -3glox Combine like terms: 12glox + -3glox = 9glox 2glo + 9glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 2glo + 9glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(2 + 9x) = 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 + 9x)' equal to zero and attempt to solve: Simplifying 2 + 9x = 0 Solving 2 + 9x = 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 + 9x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9x = 0 + -2 9x = 0 + -2 Combine like terms: 0 + -2 = -2 9x = -2 Add '-9x' to each side of the equation. 9x + -9x = -2 + -9x Combine like terms: 9x + -9x = 0 0 = -2 + -9x Simplifying 0 = -2 + -9x 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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