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Simplifying log[3](x + 2) + log[3](x + -6) = 2 Reorder the terms: glo * 3(2 + x) + log[3](x + -6) = 2 Reorder the terms for easier multiplication: 3glo(2 + x) + log[3](x + -6) = 2 (2 * 3glo + x * 3glo) + log[3](x + -6) = 2 (6glo + 3glox) + log[3](x + -6) = 2 Reorder the terms: 6glo + 3glox + glo * 3(-6 + x) = 2 Reorder the terms for easier multiplication: 6glo + 3glox + 3glo(-6 + x) = 2 6glo + 3glox + (-6 * 3glo + x * 3glo) = 2 6glo + 3glox + (-18glo + 3glox) = 2 Reorder the terms: 6glo + -18glo + 3glox + 3glox = 2 Combine like terms: 6glo + -18glo = -12glo -12glo + 3glox + 3glox = 2 Combine like terms: 3glox + 3glox = 6glox -12glo + 6glox = 2 Solving -12glo + 6glox = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + -12glo + 6glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -12glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -6glo + 3glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -6glo + 3glox)' equal to zero and attempt to solve: Simplifying -1 + -6glo + 3glox = 0 Solving -1 + -6glo + 3glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -6glo + 1 + 3glox = 0 + 1 Reorder the terms: -1 + 1 + -6glo + 3glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6glo + 3glox = 0 + 1 -6glo + 3glox = 0 + 1 Combine like terms: 0 + 1 = 1 -6glo + 3glox = 1 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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