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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 = 2glo 2glo = 2glo + -2glo + glox Combine like terms: 2glo + -2glo = 0 2glo = 0 + glox 2glo = glox Add '-1glox' to each side of the equation. 2glo + -1glox = glox + -1glox Combine like terms: glox + -1glox = 0 2glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(2 + -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. The solution to this equation could not be determined.
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