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Simplifying log(2x) + log(x + 3) = log(12x + -4) Remove parenthesis around (2x) glo * 2x + log(x + 3) = log(12x + -4) Reorder the terms for easier multiplication: 2glo * x + log(x + 3) = log(12x + -4) Multiply glo * x 2glox + log(x + 3) = log(12x + -4) Reorder the terms: 2glox + glo(3 + x) = log(12x + -4) 2glox + (3 * glo + x * glo) = log(12x + -4) 2glox + (3glo + glox) = log(12x + -4) Reorder the terms: 3glo + 2glox + glox = log(12x + -4) Combine like terms: 2glox + glox = 3glox 3glo + 3glox = log(12x + -4) Reorder the terms: 3glo + 3glox = glo(-4 + 12x) 3glo + 3glox = (-4 * glo + 12x * glo) 3glo + 3glox = (-4glo + 12glox) Solving 3glo + 3glox = -4glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4glo' to each side of the equation. 3glo + 4glo + 3glox = -4glo + 4glo + 12glox Combine like terms: 3glo + 4glo = 7glo 7glo + 3glox = -4glo + 4glo + 12glox Combine like terms: -4glo + 4glo = 0 7glo + 3glox = 0 + 12glox 7glo + 3glox = 12glox Add '-12glox' to each side of the equation. 7glo + 3glox + -12glox = 12glox + -12glox Combine like terms: 3glox + -12glox = -9glox 7glo + -9glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 7glo + -9glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(7 + -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 '(7 + -9x)' equal to zero and attempt to solve: Simplifying 7 + -9x = 0 Solving 7 + -9x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -9x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9x = 0 + -7 -9x = 0 + -7 Combine like terms: 0 + -7 = -7 -9x = -7 Add '9x' to each side of the equation. -9x + 9x = -7 + 9x Combine like terms: -9x + 9x = 0 0 = -7 + 9x Simplifying 0 = -7 + 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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