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Simplifying logx + log(x + -12) = log(17x) Reorder the terms: glox + glo(-12 + x) = log(17x) glox + (-12 * glo + x * glo) = log(17x) glox + (-12glo + glox) = log(17x) Reorder the terms: -12glo + glox + glox = log(17x) Combine like terms: glox + glox = 2glox -12glo + 2glox = log(17x) Remove parenthesis around (17x) -12glo + 2glox = glo * 17x Reorder the terms for easier multiplication: -12glo + 2glox = 17glo * x Multiply glo * x -12glo + 2glox = 17glox Solving -12glo + 2glox = 17glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-17glox' to each side of the equation. -12glo + 2glox + -17glox = 17glox + -17glox Combine like terms: 2glox + -17glox = -15glox -12glo + -15glox = 17glox + -17glox Combine like terms: 17glox + -17glox = 0 -12glo + -15glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(4 + 5x) = 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 '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Add '-5x' to each side of the equation. 5x + -5x = -4 + -5x Combine like terms: 5x + -5x = 0 0 = -4 + -5x Simplifying 0 = -4 + -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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