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Simplifying log[9] * x + log[9](x + 3) = log[9](x + 15) Reorder the terms for easier multiplication: 9glo * x + log[9](x + 3) = log[9](x + 15) Multiply glo * x 9glox + log[9](x + 3) = log[9](x + 15) Reorder the terms: 9glox + glo * 9(3 + x) = log[9](x + 15) Reorder the terms for easier multiplication: 9glox + 9glo(3 + x) = log[9](x + 15) 9glox + (3 * 9glo + x * 9glo) = log[9](x + 15) 9glox + (27glo + 9glox) = log[9](x + 15) Reorder the terms: 27glo + 9glox + 9glox = log[9](x + 15) Combine like terms: 9glox + 9glox = 18glox 27glo + 18glox = log[9](x + 15) Reorder the terms: 27glo + 18glox = glo * 9(15 + x) Reorder the terms for easier multiplication: 27glo + 18glox = 9glo(15 + x) 27glo + 18glox = (15 * 9glo + x * 9glo) 27glo + 18glox = (135glo + 9glox) Solving 27glo + 18glox = 135glo + 9glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-135glo' to each side of the equation. 27glo + -135glo + 18glox = 135glo + -135glo + 9glox Combine like terms: 27glo + -135glo = -108glo -108glo + 18glox = 135glo + -135glo + 9glox Combine like terms: 135glo + -135glo = 0 -108glo + 18glox = 0 + 9glox -108glo + 18glox = 9glox Add '-9glox' to each side of the equation. -108glo + 18glox + -9glox = 9glox + -9glox Combine like terms: 18glox + -9glox = 9glox -108glo + 9glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 -108glo + 9glox = 0 Factor out the Greatest Common Factor (GCF), '9glo'. 9glo(-12 + x) = 0 Ignore the factor 9.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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -1x 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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