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Simplifying log(x + 2) + -1log(x) = log(x + 5) Reorder the terms: glo(2 + x) + -1log(x) = log(x + 5) (2 * glo + x * glo) + -1log(x) = log(x + 5) (2glo + glox) + -1log(x) = log(x + 5) Multiply glo * x 2glo + glox + -1glox = log(x + 5) Combine like terms: glox + -1glox = 0 2glo + 0 = log(x + 5) 2glo = log(x + 5) Reorder the terms: 2glo = glo(5 + x) 2glo = (5 * glo + x * glo) 2glo = (5glo + glox) Solving 2glo = 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. 2glo + -5glo = 5glo + -5glo + glox Combine like terms: 2glo + -5glo = -3glo -3glo = 5glo + -5glo + glox Combine like terms: 5glo + -5glo = 0 -3glo = 0 + glox -3glo = glox Add '-1glox' to each side of the equation. -3glo + -1glox = glox + -1glox Combine like terms: glox + -1glox = 0 -3glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(3 + 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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