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Simplifying logx + log(x + -19) = log(19x) Reorder the terms: glox + glo(-19 + x) = log(19x) glox + (-19 * glo + x * glo) = log(19x) glox + (-19glo + glox) = log(19x) Reorder the terms: -19glo + glox + glox = log(19x) Combine like terms: glox + glox = 2glox -19glo + 2glox = log(19x) Remove parenthesis around (19x) -19glo + 2glox = glo * 19x Reorder the terms for easier multiplication: -19glo + 2glox = 19glo * x Multiply glo * x -19glo + 2glox = 19glox Solving -19glo + 2glox = 19glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-19glox' to each side of the equation. -19glo + 2glox + -19glox = 19glox + -19glox Combine like terms: 2glox + -19glox = -17glox -19glo + -17glox = 19glox + -19glox Combine like terms: 19glox + -19glox = 0 -19glo + -17glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(19 + 17x) = 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 '(19 + 17x)' equal to zero and attempt to solve: Simplifying 19 + 17x = 0 Solving 19 + 17x = 0 Move all terms containing g to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 17x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 17x = 0 + -19 17x = 0 + -19 Combine like terms: 0 + -19 = -19 17x = -19 Add '-17x' to each side of the equation. 17x + -17x = -19 + -17x Combine like terms: 17x + -17x = 0 0 = -19 + -17x Simplifying 0 = -19 + -17x 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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