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Simplifying log(x + 1) + 2log(x) = log(x2 + 8) Reorder the terms: glo(1 + x) + 2log(x) = log(x2 + 8) (1 * glo + x * glo) + 2log(x) = log(x2 + 8) (1glo + glox) + 2log(x) = log(x2 + 8) Multiply glo * x 1glo + glox + 2glox = log(x2 + 8) Combine like terms: glox + 2glox = 3glox 1glo + 3glox = log(x2 + 8) Reorder the terms: 1glo + 3glox = glo(8 + x2) 1glo + 3glox = (8 * glo + x2 * glo) 1glo + 3glox = (8glo + glox2) Solving 1glo + 3glox = 8glo + glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. 1glo + -8glo + 3glox = 8glo + -8glo + glox2 Combine like terms: 1glo + -8glo = -7glo -7glo + 3glox = 8glo + -8glo + glox2 Combine like terms: 8glo + -8glo = 0 -7glo + 3glox = 0 + glox2 -7glo + 3glox = glox2 Add '-1glox2' to each side of the equation. -7glo + 3glox + -1glox2 = glox2 + -1glox2 Combine like terms: glox2 + -1glox2 = 0 -7glo + 3glox + -1glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-7 + 3x + -1x2) = 0Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-7 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -7 + 3x + -1x2 = 0 Solving -7 + 3x + -1x2 = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 3x + 7 + -1x2 = 0 + 7 Reorder the terms: -7 + 7 + 3x + -1x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x + -1x2 = 0 + 7 3x + -1x2 = 0 + 7 Combine like terms: 0 + 7 = 7 3x + -1x2 = 7 Add '-3x' to each side of the equation. 3x + -3x + -1x2 = 7 + -3x Combine like terms: 3x + -3x = 0 0 + -1x2 = 7 + -3x -1x2 = 7 + -3x Add 'x2' to each side of the equation. -1x2 + x2 = 7 + -3x + x2 Combine like terms: -1x2 + x2 = 0 0 = 7 + -3x + x2 Simplifying 0 = 7 + -3x + x2 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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