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Simplifying log(x) + log(x + -4) = log(12x) Multiply glo * x glox + log(x + -4) = log(12x) Reorder the terms: glox + glo(-4 + x) = log(12x) glox + (-4 * glo + x * glo) = log(12x) glox + (-4glo + glox) = log(12x) Reorder the terms: -4glo + glox + glox = log(12x) Combine like terms: glox + glox = 2glox -4glo + 2glox = log(12x) Remove parenthesis around (12x) -4glo + 2glox = glo * 12x Reorder the terms for easier multiplication: -4glo + 2glox = 12glo * x Multiply glo * x -4glo + 2glox = 12glox Solving -4glo + 2glox = 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glox' to each side of the equation. -4glo + 2glox + -12glox = 12glox + -12glox Combine like terms: 2glox + -12glox = -10glox -4glo + -10glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -4glo + -10glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(2 + 5x) = 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 '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Add '-5x' to each side of the equation. 5x + -5x = -2 + -5x Combine like terms: 5x + -5x = 0 0 = -2 + -5x Simplifying 0 = -2 + -5x 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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