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Simplifying log(3x + -3) = log(x + 1) + log(4) Reorder the terms: glo(-3 + 3x) = log(x + 1) + log(4) (-3 * glo + 3x * glo) = log(x + 1) + log(4) (-3glo + 3glox) = log(x + 1) + log(4) Reorder the terms: -3glo + 3glox = glo(1 + x) + log(4) -3glo + 3glox = (1 * glo + x * glo) + log(4) -3glo + 3glox = (1glo + glox) + log(4) Reorder the terms for easier multiplication: -3glo + 3glox = 1glo + glox + 4glo Reorder the terms: -3glo + 3glox = 1glo + 4glo + glox Combine like terms: 1glo + 4glo = 5glo -3glo + 3glox = 5glo + glox Solving -3glo + 3glox = 5glo + glox 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. -3glo + -5glo + 3glox = 5glo + -5glo + glox Combine like terms: -3glo + -5glo = -8glo -8glo + 3glox = 5glo + -5glo + glox Combine like terms: 5glo + -5glo = 0 -8glo + 3glox = 0 + glox -8glo + 3glox = glox Add '-1glox' to each side of the equation. -8glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox -8glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 0 -8glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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