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