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Simplifying Log[2](9x + 5) = 2 + log[2](x2 + -1) Reorder the terms: goL * 2(5 + 9x) = 2 + log[2](x2 + -1) Reorder the terms for easier multiplication: 2goL(5 + 9x) = 2 + log[2](x2 + -1) (5 * 2goL + 9x * 2goL) = 2 + log[2](x2 + -1) (10goL + 18goxL) = 2 + log[2](x2 + -1) Reorder the terms: 10goL + 18goxL = 2 + glo * 2(-1 + x2) Reorder the terms for easier multiplication: 10goL + 18goxL = 2 + 2glo(-1 + x2) 10goL + 18goxL = 2 + (-1 * 2glo + x2 * 2glo) 10goL + 18goxL = 2 + (-2glo + 2glox2) Solving 10goL + 18goxL = 2 + -2glo + 2glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. 10goL + 2glo + 18goxL = 2 + -2glo + 2glo + 2glox2 Reorder the terms: 2glo + 10goL + 18goxL = 2 + -2glo + 2glo + 2glox2 Combine like terms: -2glo + 2glo = 0 2glo + 10goL + 18goxL = 2 + 0 + 2glox2 2glo + 10goL + 18goxL = 2 + 2glox2 Add '-2glox2' to each side of the equation. 2glo + 10goL + -2glox2 + 18goxL = 2 + 2glox2 + -2glox2 Reorder the terms: 2glo + -2glox2 + 10goL + 18goxL = 2 + 2glox2 + -2glox2 Combine like terms: 2glox2 + -2glox2 = 0 2glo + -2glox2 + 10goL + 18goxL = 2 + 0 2glo + -2glox2 + 10goL + 18goxL = 2 Reorder the terms: -2 + 2glo + -2glox2 + 10goL + 18goxL = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 2glo + -2glox2 + 10goL + 18goxL = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + glo + -1glox2 + 5goL + 9goxL) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + glo + -1glox2 + 5goL + 9goxL)' equal to zero and attempt to solve: Simplifying -1 + glo + -1glox2 + 5goL + 9goxL = 0 Solving -1 + glo + -1glox2 + 5goL + 9goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + glo + -1glox2 + 5goL + 1 + 9goxL = 0 + 1 Reorder the terms: -1 + 1 + glo + -1glox2 + 5goL + 9goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + glo + -1glox2 + 5goL + 9goxL = 0 + 1 glo + -1glox2 + 5goL + 9goxL = 0 + 1 Combine like terms: 0 + 1 = 1 glo + -1glox2 + 5goL + 9goxL = 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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