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