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Simplifying log(x + 2) + log(x + -3) = log(x + 29) Reorder the terms: glo(2 + x) + log(x + -3) = log(x + 29) (2 * glo + x * glo) + log(x + -3) = log(x + 29) (2glo + glox) + log(x + -3) = log(x + 29) Reorder the terms: 2glo + glox + glo(-3 + x) = log(x + 29) 2glo + glox + (-3 * glo + x * glo) = log(x + 29) 2glo + glox + (-3glo + glox) = log(x + 29) Reorder the terms: 2glo + -3glo + glox + glox = log(x + 29) Combine like terms: 2glo + -3glo = -1glo -1glo + glox + glox = log(x + 29) Combine like terms: glox + glox = 2glox -1glo + 2glox = log(x + 29) Reorder the terms: -1glo + 2glox = glo(29 + x) -1glo + 2glox = (29 * glo + x * glo) -1glo + 2glox = (29glo + glox) Solving -1glo + 2glox = 29glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-29glo' to each side of the equation. -1glo + -29glo + 2glox = 29glo + -29glo + glox Combine like terms: -1glo + -29glo = -30glo -30glo + 2glox = 29glo + -29glo + glox Combine like terms: 29glo + -29glo = 0 -30glo + 2glox = 0 + glox -30glo + 2glox = glox Add '-1glox' to each side of the equation. -30glo + 2glox + -1glox = glox + -1glox Combine like terms: 2glox + -1glox = 1glox -30glo + 1glox = glox + -1glox Combine like terms: glox + -1glox = 0 -30glo + 1glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(-30 + x) = 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 '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Add '-1x' to each side of the equation. x + -1x = 30 + -1x Combine like terms: x + -1x = 0 0 = 30 + -1x Simplifying 0 = 30 + -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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