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Simplifying 2logx + -1log(1 + -1x) = log(2 + -1x) 2glox + (1 * -1glo + -1x * -1glo) = log(2 + -1x) 2glox + (-1glo + 1glox) = log(2 + -1x) Reorder the terms: -1glo + 2glox + 1glox = log(2 + -1x) Combine like terms: 2glox + 1glox = 3glox -1glo + 3glox = log(2 + -1x) -1glo + 3glox = (2 * glo + -1x * glo) -1glo + 3glox = (2glo + -1glox) Solving -1glo + 3glox = 2glo + -1glox 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 + 3glox = 2glo + -2glo + -1glox Combine like terms: -1glo + -2glo = -3glo -3glo + 3glox = 2glo + -2glo + -1glox Combine like terms: 2glo + -2glo = 0 -3glo + 3glox = 0 + -1glox -3glo + 3glox = -1glox Add 'glox' to each side of the equation. -3glo + 3glox + glox = -1glox + glox Combine like terms: 3glox + glox = 4glox -3glo + 4glox = -1glox + glox Combine like terms: -1glox + glox = 0 -3glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-3 + 4x) = 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 '(-3 + 4x)' equal to zero and attempt to solve: Simplifying -3 + 4x = 0 Solving -3 + 4x = 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 + 4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x = 0 + 3 4x = 0 + 3 Combine like terms: 0 + 3 = 3 4x = 3 Add '-4x' to each side of the equation. 4x + -4x = 3 + -4x Combine like terms: 4x + -4x = 0 0 = 3 + -4x Simplifying 0 = 3 + -4x 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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