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