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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), 'glo'. glo(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + 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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