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Simplifying log[2](12x + 8) = 2 + log[2](x + 3) Reorder the terms: glo * 2(8 + 12x) = 2 + log[2](x + 3) Reorder the terms for easier multiplication: 2glo(8 + 12x) = 2 + log[2](x + 3) (8 * 2glo + 12x * 2glo) = 2 + log[2](x + 3) (16glo + 24glox) = 2 + log[2](x + 3) Reorder the terms: 16glo + 24glox = 2 + glo * 2(3 + x) Reorder the terms for easier multiplication: 16glo + 24glox = 2 + 2glo(3 + x) 16glo + 24glox = 2 + (3 * 2glo + x * 2glo) 16glo + 24glox = 2 + (6glo + 2glox) Solving 16glo + 24glox = 2 + 6glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6glo' to each side of the equation. 16glo + -6glo + 24glox = 2 + 6glo + -6glo + 2glox Combine like terms: 16glo + -6glo = 10glo 10glo + 24glox = 2 + 6glo + -6glo + 2glox Combine like terms: 6glo + -6glo = 0 10glo + 24glox = 2 + 0 + 2glox 10glo + 24glox = 2 + 2glox Add '-2glox' to each side of the equation. 10glo + 24glox + -2glox = 2 + 2glox + -2glox Combine like terms: 24glox + -2glox = 22glox 10glo + 22glox = 2 + 2glox + -2glox Combine like terms: 2glox + -2glox = 0 10glo + 22glox = 2 + 0 10glo + 22glox = 2 Reorder the terms: -2 + 10glo + 22glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 10glo + 22glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 5glo + 11glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 5glo + 11glox)' equal to zero and attempt to solve: Simplifying -1 + 5glo + 11glox = 0 Solving -1 + 5glo + 11glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 5glo + 1 + 11glox = 0 + 1 Reorder the terms: -1 + 1 + 5glo + 11glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5glo + 11glox = 0 + 1 5glo + 11glox = 0 + 1 Combine like terms: 0 + 1 = 1 5glo + 11glox = 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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