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Simplifying logx + log(x + -18) = log(6x) Reorder the terms: glox + glo(-18 + x) = log(6x) glox + (-18 * glo + x * glo) = log(6x) glox + (-18glo + glox) = log(6x) Reorder the terms: -18glo + glox + glox = log(6x) Combine like terms: glox + glox = 2glox -18glo + 2glox = log(6x) Remove parenthesis around (6x) -18glo + 2glox = glo * 6x Reorder the terms for easier multiplication: -18glo + 2glox = 6glo * x Multiply glo * x -18glo + 2glox = 6glox Solving -18glo + 2glox = 6glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glox' to each side of the equation. -18glo + 2glox + -6glox = 6glox + -6glox Combine like terms: 2glox + -6glox = -4glox -18glo + -4glox = 6glox + -6glox Combine like terms: 6glox + -6glox = 0 -18glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-2glo'. -2glo(9 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 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 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Add '-2x' to each side of the equation. 2x + -2x = -9 + -2x Combine like terms: 2x + -2x = 0 0 = -9 + -2x Simplifying 0 = -9 + -2x 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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