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Simplifying logx + log(x + -7) = log(18x) Reorder the terms: glox + glo(-7 + x) = log(18x) glox + (-7 * glo + x * glo) = log(18x) glox + (-7glo + glox) = log(18x) Reorder the terms: -7glo + glox + glox = log(18x) Combine like terms: glox + glox = 2glox -7glo + 2glox = log(18x) Remove parenthesis around (18x) -7glo + 2glox = glo * 18x Reorder the terms for easier multiplication: -7glo + 2glox = 18glo * x Multiply glo * x -7glo + 2glox = 18glox Solving -7glo + 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. -7glo + 2glox + -18glox = 18glox + -18glox Combine like terms: 2glox + -18glox = -16glox -7glo + -16glox = 18glox + -18glox Combine like terms: 18glox + -18glox = 0 -7glo + -16glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(7 + 16x) = 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 '(7 + 16x)' equal to zero and attempt to solve: Simplifying 7 + 16x = 0 Solving 7 + 16x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 16x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 16x = 0 + -7 16x = 0 + -7 Combine like terms: 0 + -7 = -7 16x = -7 Add '-16x' to each side of the equation. 16x + -16x = -7 + -16x Combine like terms: 16x + -16x = 0 0 = -7 + -16x Simplifying 0 = -7 + -16x 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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