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Simplifying log[2](12x + 6) = 3 + log[2](x + 4) Reorder the terms: glo * 2(6 + 12x) = 3 + log[2](x + 4) Reorder the terms for easier multiplication: 2glo(6 + 12x) = 3 + log[2](x + 4) (6 * 2glo + 12x * 2glo) = 3 + log[2](x + 4) (12glo + 24glox) = 3 + log[2](x + 4) Reorder the terms: 12glo + 24glox = 3 + glo * 2(4 + x) Reorder the terms for easier multiplication: 12glo + 24glox = 3 + 2glo(4 + x) 12glo + 24glox = 3 + (4 * 2glo + x * 2glo) 12glo + 24glox = 3 + (8glo + 2glox) Solving 12glo + 24glox = 3 + 8glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. 12glo + -8glo + 24glox = 3 + 8glo + -8glo + 2glox Combine like terms: 12glo + -8glo = 4glo 4glo + 24glox = 3 + 8glo + -8glo + 2glox Combine like terms: 8glo + -8glo = 0 4glo + 24glox = 3 + 0 + 2glox 4glo + 24glox = 3 + 2glox Add '-2glox' to each side of the equation. 4glo + 24glox + -2glox = 3 + 2glox + -2glox Combine like terms: 24glox + -2glox = 22glox 4glo + 22glox = 3 + 2glox + -2glox Combine like terms: 2glox + -2glox = 0 4glo + 22glox = 3 + 0 4glo + 22glox = 3 Reorder the terms: -3 + 4glo + 22glox = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 4glo + 22glox = 0 The solution to this equation could not be determined.
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