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Simplifying log(4 + -1x) = log(x + 8) + log(2x + 13) (4 * glo + -1x * glo) = log(x + 8) + log(2x + 13) (4glo + -1glox) = log(x + 8) + log(2x + 13) Reorder the terms: 4glo + -1glox = glo(8 + x) + log(2x + 13) 4glo + -1glox = (8 * glo + x * glo) + log(2x + 13) 4glo + -1glox = (8glo + glox) + log(2x + 13) Reorder the terms: 4glo + -1glox = 8glo + glox + glo(13 + 2x) 4glo + -1glox = 8glo + glox + (13 * glo + 2x * glo) 4glo + -1glox = 8glo + glox + (13glo + 2glox) Reorder the terms: 4glo + -1glox = 8glo + 13glo + glox + 2glox Combine like terms: 8glo + 13glo = 21glo 4glo + -1glox = 21glo + glox + 2glox Combine like terms: glox + 2glox = 3glox 4glo + -1glox = 21glo + 3glox Solving 4glo + -1glox = 21glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-21glo' to each side of the equation. 4glo + -21glo + -1glox = 21glo + -21glo + 3glox Combine like terms: 4glo + -21glo = -17glo -17glo + -1glox = 21glo + -21glo + 3glox Combine like terms: 21glo + -21glo = 0 -17glo + -1glox = 0 + 3glox -17glo + -1glox = 3glox Add '-3glox' to each side of the equation. -17glo + -1glox + -3glox = 3glox + -3glox Combine like terms: -1glox + -3glox = -4glox -17glo + -4glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 -17glo + -4glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(17 + 4x) = 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 '(17 + 4x)' equal to zero and attempt to solve: Simplifying 17 + 4x = 0 Solving 17 + 4x = 0 Move all terms containing g to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 4x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 4x = 0 + -17 4x = 0 + -17 Combine like terms: 0 + -17 = -17 4x = -17 Add '-4x' to each side of the equation. 4x + -4x = -17 + -4x Combine like terms: 4x + -4x = 0 0 = -17 + -4x Simplifying 0 = -17 + -4x 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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