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Simplifying logx + log(x + -18) = log(18x) Reorder the terms: glox + glo(-18 + x) = log(18x) glox + (-18 * glo + x * glo) = log(18x) glox + (-18glo + glox) = log(18x) Reorder the terms: -18glo + glox + glox = log(18x) Combine like terms: glox + glox = 2glox -18glo + 2glox = log(18x) Remove parenthesis around (18x) -18glo + 2glox = glo * 18x Reorder the terms for easier multiplication: -18glo + 2glox = 18glo * x Multiply glo * x -18glo + 2glox = 18glox Solving -18glo + 2glox = 18glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-18glox' to each side of the equation. -18glo + 2glox + -18glox = 18glox + -18glox Combine like terms: 2glox + -18glox = -16glox -18glo + -16glox = 18glox + -18glox Combine like terms: 18glox + -18glox = 0 -18glo + -16glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(9 + 8x) = 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 '(9 + 8x)' equal to zero and attempt to solve: Simplifying 9 + 8x = 0 Solving 9 + 8x = 0 Move all terms containing g to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x = 0 + -9 8x = 0 + -9 Combine like terms: 0 + -9 = -9 8x = -9 Add '-8x' to each side of the equation. 8x + -8x = -9 + -8x Combine like terms: 8x + -8x = 0 0 = -9 + -8x Simplifying 0 = -9 + -8x 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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