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Simplifying log(x + 5) + -1log(4 + -1x) + log(3x + -1) = log(3x + -1) + -1log(x + 4) Reorder the terms: glo(5 + x) + -1log(4 + -1x) + log(3x + -1) = log(3x + -1) + -1log(x + 4) (5 * glo + x * glo) + -1log(4 + -1x) + log(3x + -1) = log(3x + -1) + -1log(x + 4) (5glo + glox) + -1log(4 + -1x) + log(3x + -1) = log(3x + -1) + -1log(x + 4) 5glo + glox + (4 * -1glo + -1x * -1glo) + log(3x + -1) = log(3x + -1) + -1log(x + 4) 5glo + glox + (-4glo + 1glox) + log(3x + -1) = log(3x + -1) + -1log(x + 4) Reorder the terms: 5glo + glox + -4glo + 1glox + glo(-1 + 3x) = log(3x + -1) + -1log(x + 4) 5glo + glox + -4glo + 1glox + (-1 * glo + 3x * glo) = log(3x + -1) + -1log(x + 4) 5glo + glox + -4glo + 1glox + (-1glo + 3glox) = log(3x + -1) + -1log(x + 4) Reorder the terms: 5glo + -4glo + -1glo + glox + 1glox + 3glox = log(3x + -1) + -1log(x + 4) Combine like terms: 5glo + -4glo = 1glo 1glo + -1glo + glox + 1glox + 3glox = log(3x + -1) + -1log(x + 4) Combine like terms: 1glo + -1glo = 0 0 + glox + 1glox + 3glox = log(3x + -1) + -1log(x + 4) glox + 1glox + 3glox = log(3x + -1) + -1log(x + 4) Combine like terms: glox + 1glox = 2glox 2glox + 3glox = log(3x + -1) + -1log(x + 4) Combine like terms: 2glox + 3glox = 5glox 5glox = log(3x + -1) + -1log(x + 4) Reorder the terms: 5glox = glo(-1 + 3x) + -1log(x + 4) 5glox = (-1 * glo + 3x * glo) + -1log(x + 4) 5glox = (-1glo + 3glox) + -1log(x + 4) Reorder the terms: 5glox = -1glo + 3glox + -1glo(4 + x) 5glox = -1glo + 3glox + (4 * -1glo + x * -1glo) 5glox = -1glo + 3glox + (-4glo + -1glox) Reorder the terms: 5glox = -1glo + -4glo + 3glox + -1glox Combine like terms: -1glo + -4glo = -5glo 5glox = -5glo + 3glox + -1glox Combine like terms: 3glox + -1glox = 2glox 5glox = -5glo + 2glox Solving 5glox = -5glo + 2glox 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. 5glo + 5glox = -5glo + 5glo + 2glox Combine like terms: -5glo + 5glo = 0 5glo + 5glox = 0 + 2glox 5glo + 5glox = 2glox Add '-2glox' to each side of the equation. 5glo + 5glox + -2glox = 2glox + -2glox Combine like terms: 5glox + -2glox = 3glox 5glo + 3glox = 2glox + -2glox Combine like terms: 2glox + -2glox = 0 5glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), 'glo'. glo(5 + 3x) = 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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Add '-3x' to each side of the equation. 3x + -3x = -5 + -3x Combine like terms: 3x + -3x = 0 0 = -5 + -3x Simplifying 0 = -5 + -3x 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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