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Simplifying log(3x) + log(x + 2) = log(9x2 + 18x) Remove parenthesis around (3x) glo * 3x + log(x + 2) = log(9x2 + 18x) Reorder the terms for easier multiplication: 3glo * x + log(x + 2) = log(9x2 + 18x) Multiply glo * x 3glox + log(x + 2) = log(9x2 + 18x) Reorder the terms: 3glox + glo(2 + x) = log(9x2 + 18x) 3glox + (2 * glo + x * glo) = log(9x2 + 18x) 3glox + (2glo + glox) = log(9x2 + 18x) Reorder the terms: 2glo + 3glox + glox = log(9x2 + 18x) Combine like terms: 3glox + glox = 4glox 2glo + 4glox = log(9x2 + 18x) Reorder the terms: 2glo + 4glox = glo(18x + 9x2) 2glo + 4glox = (18x * glo + 9x2 * glo) 2glo + 4glox = (18glox + 9glox2) Solving 2glo + 4glox = 18glox + 9glox2 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. 2glo + 4glox + -18glox = 18glox + -18glox + 9glox2 Combine like terms: 4glox + -18glox = -14glox 2glo + -14glox = 18glox + -18glox + 9glox2 Combine like terms: 18glox + -18glox = 0 2glo + -14glox = 0 + 9glox2 2glo + -14glox = 9glox2 Add '-9glox2' to each side of the equation. 2glo + -14glox + -9glox2 = 9glox2 + -9glox2 Combine like terms: 9glox2 + -9glox2 = 0 2glo + -14glox + -9glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(2 + -14x + -9x2) = 0Subproblem 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 '(2 + -14x + -9x2)' equal to zero and attempt to solve: Simplifying 2 + -14x + -9x2 = 0 Solving 2 + -14x + -9x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -14x + -2 + -9x2 = 0 + -2 Reorder the terms: 2 + -2 + -14x + -9x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -14x + -9x2 = 0 + -2 -14x + -9x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -14x + -9x2 = -2 Add '14x' to each side of the equation. -14x + 14x + -9x2 = -2 + 14x Combine like terms: -14x + 14x = 0 0 + -9x2 = -2 + 14x -9x2 = -2 + 14x Add '9x2' to each side of the equation. -9x2 + 9x2 = -2 + 14x + 9x2 Combine like terms: -9x2 + 9x2 = 0 0 = -2 + 14x + 9x2 Simplifying 0 = -2 + 14x + 9x2 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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