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