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Simplifying log(x + -4) + -1log(x) = log(x + 2) Reorder the terms: glo(-4 + x) + -1log(x) = log(x + 2) (-4 * glo + x * glo) + -1log(x) = log(x + 2) (-4glo + glox) + -1log(x) = log(x + 2) Multiply glo * x -4glo + glox + -1glox = log(x + 2) Combine like terms: glox + -1glox = 0 -4glo + 0 = log(x + 2) -4glo = log(x + 2) Reorder the terms: -4glo = glo(2 + x) -4glo = (2 * glo + x * glo) -4glo = (2glo + glox) Solving -4glo = 2glo + glox 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. -4glo + -2glo = 2glo + -2glo + glox Combine like terms: -4glo + -2glo = -6glo -6glo = 2glo + -2glo + glox Combine like terms: 2glo + -2glo = 0 -6glo = 0 + glox -6glo = glox Add '-1glox' to each side of the equation. -6glo + -1glox = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(6 + x) = 0 Ignore the factor -1.Subproblem 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 '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x 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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