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Simplifying 2log(3x2 + 5x + 6) + -2log(3x + 1) = 2 Reorder the terms: 2glo(6 + 5x + 3x2) + -2log(3x + 1) = 2 (6 * 2glo + 5x * 2glo + 3x2 * 2glo) + -2log(3x + 1) = 2 (12glo + 10glox + 6glox2) + -2log(3x + 1) = 2 Reorder the terms: 12glo + 10glox + 6glox2 + -2glo(1 + 3x) = 2 12glo + 10glox + 6glox2 + (1 * -2glo + 3x * -2glo) = 2 12glo + 10glox + 6glox2 + (-2glo + -6glox) = 2 Reorder the terms: 12glo + -2glo + 10glox + -6glox + 6glox2 = 2 Combine like terms: 12glo + -2glo = 10glo 10glo + 10glox + -6glox + 6glox2 = 2 Combine like terms: 10glox + -6glox = 4glox 10glo + 4glox + 6glox2 = 2 Solving 10glo + 4glox + 6glox2 = 2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -2 + 10glo + 4glox + 6glox2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 10glo + 4glox + 6glox2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 5glo + 2glox + 3glox2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 5glo + 2glox + 3glox2)' equal to zero and attempt to solve: Simplifying -1 + 5glo + 2glox + 3glox2 = 0 Solving -1 + 5glo + 2glox + 3glox2 = 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 + 2glox + 1 + 3glox2 = 0 + 1 Reorder the terms: -1 + 1 + 5glo + 2glox + 3glox2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5glo + 2glox + 3glox2 = 0 + 1 5glo + 2glox + 3glox2 = 0 + 1 Combine like terms: 0 + 1 = 1 5glo + 2glox + 3glox2 = 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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