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Simplifying log(x) + log(x + -17) = log(12x) Multiply glo * x glox + log(x + -17) = log(12x) Reorder the terms: glox + glo(-17 + x) = log(12x) glox + (-17 * glo + x * glo) = log(12x) glox + (-17glo + glox) = log(12x) Reorder the terms: -17glo + glox + glox = log(12x) Combine like terms: glox + glox = 2glox -17glo + 2glox = log(12x) Remove parenthesis around (12x) -17glo + 2glox = glo * 12x Reorder the terms for easier multiplication: -17glo + 2glox = 12glo * x Multiply glo * x -17glo + 2glox = 12glox Solving -17glo + 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. -17glo + 2glox + -12glox = 12glox + -12glox Combine like terms: 2glox + -12glox = -10glox -17glo + -10glox = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -17glo + -10glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(17 + 10x) = 0 Ignore the factor -1.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 '(17 + 10x)' equal to zero and attempt to solve: Simplifying 17 + 10x = 0 Solving 17 + 10x = 0 Move all terms containing g to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 10x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 10x = 0 + -17 10x = 0 + -17 Combine like terms: 0 + -17 = -17 10x = -17 Add '-10x' to each side of the equation. 10x + -10x = -17 + -10x Combine like terms: 10x + -10x = 0 0 = -17 + -10x Simplifying 0 = -17 + -10x 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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