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Simplifying log(x + 3) + -1log(7 + -1x) = -1log(2) Reorder the terms: glo(3 + x) + -1log(7 + -1x) = -1log(2) (3 * glo + x * glo) + -1log(7 + -1x) = -1log(2) (3glo + glox) + -1log(7 + -1x) = -1log(2) 3glo + glox + (7 * -1glo + -1x * -1glo) = -1log(2) 3glo + glox + (-7glo + 1glox) = -1log(2) Reorder the terms: 3glo + -7glo + glox + 1glox = -1log(2) Combine like terms: 3glo + -7glo = -4glo -4glo + glox + 1glox = -1log(2) Combine like terms: glox + 1glox = 2glox -4glo + 2glox = -1log(2) Reorder the terms for easier multiplication: -4glo + 2glox = -1 * 2glo Multiply -1 * 2 -4glo + 2glox = -2glo Solving -4glo + 2glox = -2glo 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 + 2glox = -2glo + 2glo Combine like terms: -4glo + 2glo = -2glo -2glo + 2glox = -2glo + 2glo Combine like terms: -2glo + 2glo = 0 -2glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-1 + x) = 0 Ignore the factor 2.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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