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Simplifying log[2](9x + 5) = 2 + log[2](x + 2) Reorder the terms: glo * 2(5 + 9x) = 2 + log[2](x + 2) Reorder the terms for easier multiplication: 2glo(5 + 9x) = 2 + log[2](x + 2) (5 * 2glo + 9x * 2glo) = 2 + log[2](x + 2) (10glo + 18glox) = 2 + log[2](x + 2) Reorder the terms: 10glo + 18glox = 2 + glo * 2(2 + x) Reorder the terms for easier multiplication: 10glo + 18glox = 2 + 2glo(2 + x) 10glo + 18glox = 2 + (2 * 2glo + x * 2glo) 10glo + 18glox = 2 + (4glo + 2glox) Solving 10glo + 18glox = 2 + 4glo + 2glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-4glo' to each side of the equation. 10glo + -4glo + 18glox = 2 + 4glo + -4glo + 2glox Combine like terms: 10glo + -4glo = 6glo 6glo + 18glox = 2 + 4glo + -4glo + 2glox Combine like terms: 4glo + -4glo = 0 6glo + 18glox = 2 + 0 + 2glox 6glo + 18glox = 2 + 2glox Add '-2glox' to each side of the equation. 6glo + 18glox + -2glox = 2 + 2glox + -2glox Combine like terms: 18glox + -2glox = 16glox 6glo + 16glox = 2 + 2glox + -2glox Combine like terms: 2glox + -2glox = 0 6glo + 16glox = 2 + 0 6glo + 16glox = 2 Reorder the terms: -2 + 6glo + 16glox = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 6glo + 16glox = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 3glo + 8glox) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 3glo + 8glox)' equal to zero and attempt to solve: Simplifying -1 + 3glo + 8glox = 0 Solving -1 + 3glo + 8glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 3glo + 1 + 8glox = 0 + 1 Reorder the terms: -1 + 1 + 3glo + 8glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3glo + 8glox = 0 + 1 3glo + 8glox = 0 + 1 Combine like terms: 0 + 1 = 1 3glo + 8glox = 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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