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Simplifying logx + log(x + -13) = log(20x) Reorder the terms: glox + glo(-13 + x) = log(20x) glox + (-13 * glo + x * glo) = log(20x) glox + (-13glo + glox) = log(20x) Reorder the terms: -13glo + glox + glox = log(20x) Combine like terms: glox + glox = 2glox -13glo + 2glox = log(20x) Remove parenthesis around (20x) -13glo + 2glox = glo * 20x Reorder the terms for easier multiplication: -13glo + 2glox = 20glo * x Multiply glo * x -13glo + 2glox = 20glox Solving -13glo + 2glox = 20glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-20glox' to each side of the equation. -13glo + 2glox + -20glox = 20glox + -20glox Combine like terms: 2glox + -20glox = -18glox -13glo + -18glox = 20glox + -20glox Combine like terms: 20glox + -20glox = 0 -13glo + -18glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(13 + 18x) = 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 '(13 + 18x)' equal to zero and attempt to solve: Simplifying 13 + 18x = 0 Solving 13 + 18x = 0 Move all terms containing g to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 18x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 18x = 0 + -13 18x = 0 + -13 Combine like terms: 0 + -13 = -13 18x = -13 Add '-18x' to each side of the equation. 18x + -18x = -13 + -18x Combine like terms: 18x + -18x = 0 0 = -13 + -18x Simplifying 0 = -13 + -18x 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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