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Simplifying logx + log(x + -1) = log(3x + 12) Reorder the terms: glox + glo(-1 + x) = log(3x + 12) glox + (-1 * glo + x * glo) = log(3x + 12) glox + (-1glo + glox) = log(3x + 12) Reorder the terms: -1glo + glox + glox = log(3x + 12) Combine like terms: glox + glox = 2glox -1glo + 2glox = log(3x + 12) Reorder the terms: -1glo + 2glox = glo(12 + 3x) -1glo + 2glox = (12 * glo + 3x * glo) -1glo + 2glox = (12glo + 3glox) Solving -1glo + 2glox = 12glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-12glo' to each side of the equation. -1glo + -12glo + 2glox = 12glo + -12glo + 3glox Combine like terms: -1glo + -12glo = -13glo -13glo + 2glox = 12glo + -12glo + 3glox Combine like terms: 12glo + -12glo = 0 -13glo + 2glox = 0 + 3glox -13glo + 2glox = 3glox Add '-3glox' to each side of the equation. -13glo + 2glox + -3glox = 3glox + -3glox Combine like terms: 2glox + -3glox = -1glox -13glo + -1glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -13glo + -1glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(13 + x) = 0 Ignore the factor -1.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 '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Add '-1x' to each side of the equation. x + -1x = -13 + -1x Combine like terms: x + -1x = 0 0 = -13 + -1x Simplifying 0 = -13 + -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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