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Simplifying log(x2 + -1) = log(x + 5) Reorder the terms: glo(-1 + x2) = log(x + 5) (-1 * glo + x2 * glo) = log(x + 5) (-1glo + glox2) = log(x + 5) Reorder the terms: -1glo + glox2 = glo(5 + x) -1glo + glox2 = (5 * glo + x * glo) -1glo + glox2 = (5glo + glox) Solving -1glo + glox2 = 5glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glo' to each side of the equation. -1glo + -5glo + glox2 = 5glo + -5glo + glox Combine like terms: -1glo + -5glo = -6glo -6glo + glox2 = 5glo + -5glo + glox Combine like terms: 5glo + -5glo = 0 -6glo + glox2 = 0 + glox -6glo + glox2 = glox Add '-1glox' to each side of the equation. -6glo + -1glox + glox2 = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + -1glox + glox2 = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-6 + -1x + x2) = 0 Factor a trinomial. glo((-2 + -1x)(3 + -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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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