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Simplifying log(9)(3x + 14) + -1log(9)(5) = log(9)(2x) Reorder the terms: glo * 9(14 + 3x) + -1log(9)(5) = log(9)(2x) Reorder the terms for easier multiplication: 9glo(14 + 3x) + -1log(9)(5) = log(9)(2x) (14 * 9glo + 3x * 9glo) + -1log(9)(5) = log(9)(2x) (126glo + 27glox) + -1log(9)(5) = log(9)(2x) Reorder the terms for easier multiplication: 126glo + 27glox + -1 * 9 * 5glo = log(9)(2x) Multiply -1 * 9 126glo + 27glox + -9 * 5glo = log(9)(2x) Multiply -9 * 5 126glo + 27glox + -45glo = log(9)(2x) Reorder the terms: 126glo + -45glo + 27glox = log(9)(2x) Combine like terms: 126glo + -45glo = 81glo 81glo + 27glox = log(9)(2x) Remove parenthesis around (2x) 81glo + 27glox = glo * 9 * 2x Reorder the terms for easier multiplication: 81glo + 27glox = 9 * 2glo * x Multiply 9 * 2 81glo + 27glox = 18glo * x Multiply glo * x 81glo + 27glox = 18glox Solving 81glo + 27glox = 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. 81glo + 27glox + -18glox = 18glox + -18glox Combine like terms: 27glox + -18glox = 9glox 81glo + 9glox = 18glox + -18glox Combine like terms: 18glox + -18glox = 0 81glo + 9glox = 0 Factor out the Greatest Common Factor (GCF), '9glo'. 9glo(9 + 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 '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -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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