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Simplifying log(x2 + 3) = 2log(x + 1) Reorder the terms: glo(3 + x2) = 2log(x + 1) (3 * glo + x2 * glo) = 2log(x + 1) (3glo + glox2) = 2log(x + 1) Reorder the terms: 3glo + glox2 = 2glo(1 + x) 3glo + glox2 = (1 * 2glo + x * 2glo) 3glo + glox2 = (2glo + 2glox) Solving 3glo + glox2 = 2glo + 2glox 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. 3glo + -2glo + glox2 = 2glo + -2glo + 2glox Combine like terms: 3glo + -2glo = 1glo 1glo + glox2 = 2glo + -2glo + 2glox Combine like terms: 2glo + -2glo = 0 1glo + glox2 = 0 + 2glox 1glo + glox2 = 2glox Add '-2glox' to each side of the equation. 1glo + -2glox + glox2 = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 1glo + -2glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(1 + -2x + x2) = 0 Factor a trinomial. glo((1 + -1x)(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 + -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.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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