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Simplifying log[3](2x + 2) + log[3](x + 3) = log[3] * x Reorder the terms: glo * 3(2 + 2x) + log[3](x + 3) = log[3] * x Reorder the terms for easier multiplication: 3glo(2 + 2x) + log[3](x + 3) = log[3] * x (2 * 3glo + 2x * 3glo) + log[3](x + 3) = log[3] * x (6glo + 6glox) + log[3](x + 3) = log[3] * x Reorder the terms: 6glo + 6glox + glo * 3(3 + x) = log[3] * x Reorder the terms for easier multiplication: 6glo + 6glox + 3glo(3 + x) = log[3] * x 6glo + 6glox + (3 * 3glo + x * 3glo) = log[3] * x 6glo + 6glox + (9glo + 3glox) = log[3] * x Reorder the terms: 6glo + 9glo + 6glox + 3glox = log[3] * x Combine like terms: 6glo + 9glo = 15glo 15glo + 6glox + 3glox = log[3] * x Combine like terms: 6glox + 3glox = 9glox 15glo + 9glox = log[3] * x Reorder the terms for easier multiplication: 15glo + 9glox = 3glo * x Multiply glo * x 15glo + 9glox = 3glox Solving 15glo + 9glox = 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3glox' to each side of the equation. 15glo + 9glox + -3glox = 3glox + -3glox Combine like terms: 9glox + -3glox = 6glox 15glo + 6glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 15glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(5 + 2x) = 0 Ignore the factor 3.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 '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Add '-2x' to each side of the equation. 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 0 = -5 + -2x Simplifying 0 = -5 + -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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