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Simplifying log(x + 5) = log(3x + -17) Reorder the terms: glo(5 + x) = log(3x + -17) (5 * glo + x * glo) = log(3x + -17) (5glo + glox) = log(3x + -17) Reorder the terms: 5glo + glox = glo(-17 + 3x) 5glo + glox = (-17 * glo + 3x * glo) 5glo + glox = (-17glo + 3glox) Solving 5glo + glox = -17glo + 3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '17glo' to each side of the equation. 5glo + 17glo + glox = -17glo + 17glo + 3glox Combine like terms: 5glo + 17glo = 22glo 22glo + glox = -17glo + 17glo + 3glox Combine like terms: -17glo + 17glo = 0 22glo + glox = 0 + 3glox 22glo + glox = 3glox Add '-3glox' to each side of the equation. 22glo + glox + -3glox = 3glox + -3glox Combine like terms: glox + -3glox = -2glox 22glo + -2glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 0 22glo + -2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(11 + -1x) = 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 '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Add 'x' to each side of the equation. -1x + x = -11 + x Combine like terms: -1x + x = 0 0 = -11 + x Simplifying 0 = -11 + x 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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